After I set my #055671 2-outlet timer to my turn on and turn off times, I cannot get the my lamp to turn on automatically. What setting should the timer be set on ?? Auto off, Auto on? or what?

It is a very basic mechanical timer. I have 3 of them.

Remove it from the wall.
Pull the tabs up for Off and Push tabs down for On.
Set the Time by turning the dial, time to arrow.
Set the slide switch to Timer On.
Plug in the appliance.
Plug the timer into the wall socket.

Manual and Advertising is here.

GE 15119 Manual - Waterheatertimer.org

http://waterheatertimer.org > pdf > GE15119-Man...

PDF GE 15119 timer manual http://waterheatertimer.org/How-to-set-timers.html http://waterheatertimer.org/GE-timers-and-manuals.html#52012.

GE 15119 Indoor 24-Hour One-Outlet Plug-in Basic Timer ...

https://www.toolboxsupply.com > products > ge-15119...

GE Indoor 24-Hour Mechanical Timer is an easy-to-use basic timer. Ideal for lamps, seasonal lights and portable fans. Turns a lamp on/off at desired times daily, ...

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1) To use the timer:
Make sure outlet has power.
Check outlet with circuit analyzer to make sure polarity issues do not affect timer operation.
Plug timer into outlet for 1 hour until battery is charged.
Some timers have internal battery that do not need to be charged.
After battery is charged, unplug timer to set programs.
Set program(s).
Turn lamp ON and make sure bulb is good.
Leave lamp turned ON
Plug lamp into timer.
Then plug timer into outlet.

2) To program the timer, open following links for possible instruction manuals:
http://waterheatertimer.org/pdf/How-to-program-Timex-TE111.pdf
http://waterheatertimer.org/Woods-timers-and-manuals.html#Timex

Take a moment and rate answer:
And take advantage of fixya expert assistance live.
For a price, expert works with you while you work on timer or any do-it-yourself project.
Fixya is always less expensive than a service call.

Intermatic HB series timers have on-off trippers that push all the way down onto the dial.
Then you rotate dial until current time lines up with arrowhead located on inner dial.
Plug timer into outlet. Turn ON your lamp and make sure bulb is good, plug lamp into timer.
Open following link for step-by-step instructions with illustrations for setting analog timers:
http://waterheatertimer.org/How-to-set-timers.html

For digital timer:
1) Timer is defective
2) Conflicting programming so timer does not perform as expected
3) Timer not set to correct mode.
4) Program 'off' is set correctly, but program 'on' is not set or 'on' time conflicts with other programming.
5) Current time not set correctly
6) Polarity on outlet is reversed or noise on the line. Check outlet with circuit analyzer.
7) Combination of factors listed above
http://waterheatertimer.org/Woods-timers-and-manuals.html#Oval

I called First Alert @ (800) 323-9005 and they faxed me the instructions for Model LS510 which is the same and got it working. They will mail it too but not email. Choose Fixed or Random mode. Choose how many hours it will stay on after dusk. Turn your lamp off and unplug the lamp. Plug lamp into timer. Put function in Fixed or Random position. Put hours on switch to number of hours you want it remain on after dusk. Plug timer into the wall outlet. Turn the lamp's switch on and Timer's LED light should be on and the lamp should be off. Turn the lamp's switch off then on again TWICE. The second time you turn the lamp's switch on the bulb in the lamp will flach on then off quickly. This indicates that the Timer is controlling the lamp's operation. Leave the lamp switch in the ON position. The timer is now set for automatic. I hope this helps.

Following page shows GE 15075 timer and manual.
Page also shows close-up image of pins used to set on-off times.
http://waterheatertimer.org/GE-timers-and-manuals.html#15075

If this is not your timer, then add a comment with description of your timer.

To set timer:
Rotate dial clockwise until current time lines up with arrowhead located on inner dial
Click pins in and out to set on-off times.
Pins out, lights ON
Pins inward, lights OFF
I use pointed fingernail file to click pins in-and-out.

Timer switch is located on top of timer.
Set switch to TIMER ON

Turn lamp on, and leave lamp ON.
Make sure bulb is working.
Plug lamp into timer.
Plug timer into wall outlet.

To double check timer functions manually rotate timer dial clockwise to watch light turn on-off.

You can also take advantage of fixya phone support.
Fixya expert will walk you through the steps for a price.

Open following link to correctly identify product:
http://cgi.ebay.it/UTILITECH-2-OUTLET-TIMER-0148373-15-AMP-LOT-OF-4-/290468257053

Utilitec 0148373 timer is plug-in type timer.
Set on-off times by moving pins.
Pins are located on dial and stick up. They can be moved back and forth like stick-shift on car.
See example of pins at following link:
http://waterheatertimer.org/Woods-timers-and-manuals.html#Pins-tabs

Instructions:
Turn ON lamp.
Light bulb is good.
Plug lamp into timer.
Plug timer into outlet.
Move some pins outward.
Then manually rotate dial clockwise to watch how lights turn on-off.
That will tell you if lights turn on or off when pins are set outward.

To set current time, rotate dial clockwise until current time lines up with arrowhead located on inner dial.
Dial turns as time passes.
Lever on top of timer is moved to 'Timer'

Your yardstake timer has photo-eye that automatically turns lights on at dusk.
And then lights remain ON until set-time expires, or dawn arrives.
Timer automatically turns off at dawn, no matter which setting, unless timer dial set to ON
Photo-eye has to be turned away from outdoor lights or lights will blink.
That's because outdoor lights cause photo=eye to sense it's dawn, and timer turns OFF >>> a moment later photo-eye senses it's dark, and turns lights ON again.
Thus the timer turns ON-OFF.
Test this by putting black tape over photo-eye, or turning timer toward dark area. Timer should turn ON and follow set-time on dial.

Utilitec makes 2 different plug-in timers.
Utilitec 0155671 is about size of baseball and has 5 buttons and two outlets. Programming is shown on link below.
http://waterheatertimer.org/How-to-program-Utilitec-0155671.html

Utilitec 0144506 timer is small and rectangular with 5 buttons and slide switch located on top of timer. This timer can turn lights on-off once a day and has 1 outlet. 0144506 Instructions are given in steps shown below.
Also see:
http://waterheatertimer.org/How-to-program-Utilitec-0144506.html

Steps:
-Plug timer into wall for 1 hour until rechargeable battery is charged and display shows.
-If battery will not charge, then check electricity to wall outlet, if electricity is good and battery will not charge, then timer is no good.
-Lamp has to be turned on for timer to work. Check bulb if timer stops working.

-Unplug timer to set program.
-Press reset button with paper clip to remove any programming.

-Slide switch on top of timer to 'Timer'
1) Set current time
Hold down Time button
Press HOUR until current hour am-pm shows in display.
Hold down Time button
Press MIN button until current minute shows
Since this is a one-day repeat timer, no day program is available.

2) Program ON > this is when you want lamp to turn ON
Hold down ON button.
Press HOUR until ON hour with am-pm displays.
Hold down ON button.
Press MIN until ON minute displays.

2) Program OFF > this is when you want lamp to turn OFF
Hold down OFF button.
Press HOUR until OFF hour with am-pm displays.
Hold down OFF button.
Press MIN until OFF minute displays.

3) Set timer to operate
Make sure slide-switch on top of timer is set to 'Timer' to run program
Plug lamp into timer, and then plug timer into wall outlet
For manual override, move slide-switch to 'On' and light will stay ON

Open following link to correctly identify product:
http://cgi.ebay.it/UTILITECH-2-OUTLET-TIMER-0148373-15-AMP-LOT-OF-4-/290468257053

Utilitec 0148373 timer is plug-in type timer.
Set on-off times by moving pins.
Pins are located on dial and stick up. They can be moved back and forth like stick-shift on car.
See example of pins at following link:
http://waterheatertimer.org/Woods-timers-and-manuals.html#Pins-tabs

Instructions:
Turn ON lamp.
Light bulb is good.
Plug lamp into timer.
Plug timer into outlet.
Move some pins outward.
Then manually rotate dial clockwise to watch how lights turn on-off.
That will tell you if lights turn on or off when pins are set outward.

To set current time, rotate dial clockwise until current time lines up with arrowhead located on inner dial.
Dial turns as time passes.
Lever on top of timer is moved to 'Timer'