97 jetta glx 5speed...at over 10mph after lifting and reapplying the accelerator (like during normal shifting),when pushing the accelerator 1-3% down, it's like the gas or electrical gets cut off until the accelerator is about 3-5% pushed down, then jerks like the car just started running again. If you push in the clutch with the accelerator at the same "dead" position...the rpm surges from about 1300 to 2200 up and down, until you get below about 5-8 mph, then it runs smooth again.

test one , all autotmatic trans is it?
1: RPM rises fast but MPH does not as normal.
2: RPM does not rise fast , bad engine.
#1 is called a slipping trans mission or will not upshift or first gear is dead.
gears mater, to go faster than 10 the tranny must upshift.
this test is simple engine weak or tranny bad.
easy as pie to detect, ask a gear head friend for advice even hands on.
what matter most is RPM it hit doing that. 2000 , 3000 ,4000/?
If RPM goes really wild over 10mph that is bad transmission
and more tests ask

Could be a developing clutch problem or maladjustment or wear of the gear linkage - or both.

Your overflow cap is your radiator cap. What you may want to do is check the thermostat housing for a bleeder. Just in case the thermostat housing is where your upper radiator hose mets your engine. On top of it may be a bleeder valve. Let the car come up to normal temp and open the valve slightly until antifreeze comes out then tighten it up.

which engine

the clutch may burn out on those gear, check the fluid if it smell burn

there is no code......unless you're using a vag-com?
have you disconnected the battery recently? or anything of the sort. if so, you may need to align your throttle body. anyhow, disconnect the battery for 10 minutes or more. it takes at least 10 minutes for the ecu to reset, so the longer the better. now, reconnect the battery, as quickly as possible, get in and turn the key to the battery. youll hear a buzzing of sorts from the engine bay if its working. leave the key on battery for 3 minutes. the buzzing will have stopped, before 3 minutes, but after the 3 minutes, start the car. now, let it sit at idle for 3 minutes, dont touch the gas. just let it sit. after 3 minutes at idle, go for a drive and you should be all set. hope that helps.

Do you know if you have a 4L60E or a 4L80E?

The tranny's are notorious for having "small" problems before they actually let go. However, there is a sensor on the transmission that tells it when to shift as well as a couple of air and cooling sensors. Try having those tested/changed and see if that helps. If not, you may be looking at a new transmission

On my 2000 jetta glx, I had to replace both the shift knob and boot as one. It is built as one unit. You have to pull the boot up over the shift knob, break/bend a clip to "unlock" the shift knob then pull up. I hope the new knob you got has the boot built in and comes with a new clip.

you have a bad motor mount that makes the motor **** around during
shifting. fix fast because this could damage the transmission