What year model did you end up getting the harness from? Are you 100%, and I mean 100% sure, that there are no modifications, hacks, or damage to it? If it didn't come from another 1995, you may have discovered another "1995 one year only" issue, as there are quite a few.
The headlight switch backlighting coming on when you turn the key on, is normal. Your door lock and window buttons should do the same.
While you have the dash bezel off checking with your other headlight switch, look very closely at the wiring pigtail going to the switch. The 1995-up design is fairly well known for burning these wires up, but most often in situations where people have added aftermarket lights with higher wattage capsules. Still, even in the stock setup the circuit is marginal. I've seen a LOT of these burnt up in that area.
Two things to be careful of while messing with the switch - take extra special care to not bump your hazard button with the dash bezel while removing/installing; that sucker is really fragile, you don't even want to accidentally press it if you can avoid it. You may already know this. The other thing, if you end up replacing the switch, take extra care with the tabs that hold it into the bezel. That plastic is usually pretty brittle. Only bend them away from the switch the absolute bare minimum needed to release it.
Richard