's actually a fairly common problem. Check the fuses first, they may be blown. After that, yes the switch is the next place to look. I'm not really sure on the Galant, but the switch is either on the transmission itself or on the shifter. Being FWD it could be either. If that is good, than you probably (likely) have a wiring problem like a loose ground. To check it out, you need to know where that switch is. Unfortunately I can't help you there. I'd suggest tightening up all your ground wires and see if that takes care of the problem.
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