I have a 2011 MB GL450 and the rear hatch door wouldn't open unless you do it manually. It will close by the regular pushing the close button.

(1) How to fix automatic power liftgate that is not working on a Lexus RX - YouTube

In link below it was said he manually had to close by pulling down and then up a little and then down and the back up a little. The hatch was eventually closed, and it reset(read it in below link.
Lexus RX 350 Questions - The hatchback door will not close using the button on the door and it ... - CarGurus

(1) 5 SECRETS About The Lexus RX 350 Power Rear Door - YouTube

Back door - Opening, closing and locking the doors - Before driving - Lexus RX 450H User Manual - Lexus RX - Lexus manuals (lexomans.com)

Can you gain access to the latch mechanism from the inside of the vehicle. ie plastic cover of rear hatch ?

Maybe you can trip the mech to open from the inside.

Rear hatch is locked or unlocked with a key. (if equipped) • To open the rear hatch, insert the key into the lock, turn it to the unlock position and pull up the rear hatch by pressing the handle (DOOR). You can also lock/unlock the latch (but not release it) with the central door lock system. • If unlocked, the rear hatch can be opened by pressing the handle (DOOR) and pulling the hatch up. • To close the rear hatch, lower and push down the rear hatch firmly. Make sure that the rear hatch is securely latched.

sounds like something may be shorted in your rear hatch switch and when you pushed the button to open it you may have blown a fuse. I would check your fuse and make sure they are all still good. I would also try to look inside the rear hatch and check the wires and see if there is something wrong with one of them.

If your hatch opens by itself with a push of a button, you will have to replace the door open and close motor located in the left rear of car. If your hatch is manual, you will just have to replace the hatch struts.

This fix is for 2011 rear manual door.
You may experience some light turns on while driving over a bump or take a sharp turn. Your rear hatch indicator said door is opened.
The courtesy switch is located inside the rear hatch latch assembly. Nothing more but a simple thin lever line leave spring that contacts the ground pole to tell body ECU the door is opened.
The spring is so thin that it bent out of shape overtime therefore when you close the door it doesn't get pushed away from the ground pole far enough caused intermittently false door open alarm.
ALl you have to do is to remove the door latch assembly. Separate the actuator from the latch. Look into the latch you would see a copper like spring one end rests onto the ground pole. Jam your screw driver between the latch housing and spring lightly pride it away from the pole to unbend it. . Manually close the latch and look to see if it gets pushed away from the pole. If it doesn't try to unbend it again.
If you have or know how to use a ohm meter than check for continuity between spring and it housing. You should get 0.3-1.0. Ohm when the latch is open and no continuity when you closed the latch.
Any question shoot me a email constant12vdc@yahoo
ED

For Doors not getting open with remote or key problem,there are help links provided below.Click the link below to go through its procedure and troubleshoot the problem:----
drivers side front door will not open from inside or outside?

http://technoanswers.blogspot.com/2012/01/ford-f-350-crew-cab-drivers-side-front.html

----------

Car door will not close?
http://howtobyme.blogspot.com/2011/11/car-door-will-not-close.html

--------

All power door locks not working ?
http://howtobyme.blogspot.com/2011/11/all-power-door-locks-not-working-on_14.html

----------

Repairing car Door lock Actuator?
http://howtobyme.blogspot.com/2011/11/repairing-car-door-lock-actuator.html
---------------
How to Access car door panel?
http://howtobyme.blogspot.com/2011/11/how-to-access-car-door-panel.html

----------

Vehicle door panel components?

http://howtobyme.blogspot.com/2011/11/vehicle-door-panel-components.html

---------
Truck Door will not close?

http://schematicsdiagram.blogspot.com/2011/12/ford-truck-door-will-not-close.html

-----------
Where is Cars Door control Module located?

http://schematicsdiagram.blogspot.com/2011/12/where-is-cars-door-control-module.html

--------
Power door locks not working?

http://schematicsdiagram.blogspot.com/2011/12/power-door-locks-not-working.html

-----------
Door ajar light stays on?

http://technoanswers.blogspot.com/2012/01/door-ajar-light-stays-on.html

----------
Door locks not working?

http://technoanswers.blogspot.com/2012/01/door-locks-not-working-on-ford-explorer.html

----------
Front Door dis-assembly diagram?

http://repairhelpcenter.blogspot.in/2012/02/front-door-dis-assembly-diagram-for.html

---------
Rear Door dis-assembly diagram?

http://repairhelpcenter.blogspot.in/2012/02/rear-door-dis-assembly-diagram-for.html

--------
How to test Power door locks?

http://repairhelpcenter.blogspot.in/2012/02/how-to-test-power-door-locks.html

--------
Doors will not open with Remote?

http://schematicsdiagram.blogspot.in/2012/02/lexus-doors-will-not-open-with-remote.html

--------

How to replace Door Hatch ?
http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-hatch-on-acura-integra.html

---------

How to remove Doors?

http://repairhelpcenter.blogspot.com/2011/11/how-to-remove-doors-on-acura-integra.html

-------`-

How to Replace Doors?
http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-doors-on-audi-a4-and-vw.html

--------

Remote will not unlock Rear door?
http://schematicsdiagram.blogspot.com/2011/12/remote-will-not-unlock-rear-door-on-gmc.html

--------

Door locks or windows not working on car?
http://schematicsdiagram.blogspot.com/2011/07/door-locks-or-windows-not-working-on.html

--------

This will help.

Thanks.

For Doors not getting open with remote or key problem,there are help links provided below.Click the link below to go through its procedure and troubleshoot the problem:----
drivers side front door will not open from inside or outside?

http://technoanswers.blogspot.com/2012/01/ford-f-350-crew-cab-drivers-side-front.html

----------

Car door will not close?
http://howtobyme.blogspot.com/2011/11/car-door-will-not-close.html

--------

All power door locks not working ?
http://howtobyme.blogspot.com/2011/11/all-power-door-locks-not-working-on_14.html

----------

Repairing car Door lock Actuator?
http://howtobyme.blogspot.com/2011/11/repairing-car-door-lock-actuator.html
---------------
How to Access car door panel?
http://howtobyme.blogspot.com/2011/11/how-to-access-car-door-panel.html

----------

Vehicle door panel components?

http://howtobyme.blogspot.com/2011/11/vehicle-door-panel-components.html

---------
Truck Door will not close?

http://schematicsdiagram.blogspot.com/2011/12/ford-truck-door-will-not-close.html

-----------
Where is Cars Door control Module located?

http://schematicsdiagram.blogspot.com/2011/12/where-is-cars-door-control-module.html

--------
Power door locks not working?

http://schematicsdiagram.blogspot.com/2011/12/power-door-locks-not-working.html

-----------
Door ajar light stays on?

http://technoanswers.blogspot.com/2012/01/door-ajar-light-stays-on.html

----------
Door locks not working?

http://technoanswers.blogspot.com/2012/01/door-locks-not-working-on-ford-explorer.html

----------
Front Door dis-assembly diagram?

http://repairhelpcenter.blogspot.in/2012/02/front-door-dis-assembly-diagram-for.html

---------
Rear Door dis-assembly diagram?

http://repairhelpcenter.blogspot.in/2012/02/rear-door-dis-assembly-diagram-for.html

--------
How to test Power door locks?

http://repairhelpcenter.blogspot.in/2012/02/how-to-test-power-door-locks.html

--------
Doors will not open with Remote?

http://schematicsdiagram.blogspot.in/2012/02/lexus-doors-will-not-open-with-remote.html

--------

How to replace Door Hatch ?
http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-hatch-on-acura-integra.html

---------

How to remove Doors?

http://repairhelpcenter.blogspot.com/2011/11/how-to-remove-doors-on-acura-integra.html

-------`-

How to Replace Doors?
http://repairhelpcenter.blogspot.com/2011/11/how-to-replace-doors-on-audi-a4-and-vw.html

--------

Remote will not unlock Rear door?
http://schematicsdiagram.blogspot.com/2011/12/remote-will-not-unlock-rear-door-on-gmc.html

--------

Door locks or windows not working on car?
http://schematicsdiagram.blogspot.com/2011/07/door-locks-or-windows-not-working-on.html

--------

This will help.

Thanks.

With regards to the lock bittons on the driver and passenger side its the button themselves aka switch(s) that is your culprit. Why because the remote is getting the motor to open and close them . The only thing that doesn't is the buttons /switches themselves .
Now the rear latch a little different animal. Either the locking mechanism on the door itself is defective or the motor ( the thing you hear clicking) is weak.
This one your gonna need a shop manual for to do the correct testing.But being that te remote will not move it and neither will the manual push button I would lean towards the locking mechanism on the hatch/door its self. Use the shop manual its not that bad of a fix if you have a little patience.

I don't have any beetle experience, but there should be a little 'button' around the door of the hatch (all car doors have this). When the door is closed (or hatch), the door pushes the button in which breaks the electric circuit and turns the light off. When the door is opened, the button pops out and the circuit is complete, which turns the light on. Look for this 'button' around the hatch area, see if it's damaged (bent over) which would keep the circuit open, and the light on. Good luck, countrycurt0