I just repaired some wiring and put in a new bulb for my shifter indicator light, since it wasn't working. I noticed that this light stays on all of the time while the car is on. I was wondering if its only supposed to be on when my lights are on, or if its supposed to stay on all the time when the car is running. Which is it?

 

I can't tell cause all of the wires that go to it come from the light switch. blue blk wire goes to the light from the light switch and the source is the blk org wire that also feeds the door courtesy lights.

 

If the wire is blue/red stripe it goes on with the headlight switch .

I forget what colour that wire is.

 

That shifter light should be ON all the time. (When the key is on.) "Blue-red" wire!

The courtesy lights are feed by the "Black-blue" wire.

 

I was sure it was turned on with the key

The Transmission indicator light is not a courtesy light.

Yes and the blue/Red wire is for instrumentation and dash.
On ford trucks and car the Gear selector light was part of that instrumentation circuit