In that case, I would have to agree with the shop, it is electrical.
That light is connected to a switch on the t-case (I think it's actually on the shift motor) that detects which position the shift motor is in. When the t-case is in 2H, no lights are supposed to be on, in 4H - the 4x4 light comes on, in 4L - the 4x4 and lowrange lights come on. I haven't had to deal with problems with just the lights before, so I don't know the specifics, but if you get a wiring diagram, you should be able to go through it and find the fault. There might also be some kind of adjustment at the shift motor to properly set the detector switch. Hopefully someone can shed more light on it.