I have a 99 Z24 and none of these are working. No clicking, and no indicators when I switch them on. Also when the car is running, the High beam indicator is lit up, and when I turn the lights on, the turn signal indicators light up, when I switch either side on with the lights on, the indicators go out. From what I've read, it sounds like the combination switch.
I know it's super late, and you probably fixed this, but its 1 am and I am bored, so check your ground under your battery tray, it is bolted to the "frame rail." It is known to corrode and cause weird electrical problems.
- Your not-so-local, untrained, uncertified, backyard mechanic. But my @!#$ runs