The GEN2 bulb should be a 194 3w bulb. the 168s are 5w. (you can find the bulb numbers in the parts manuals)
Next time you take it out, check the socket itself. The tabs are know to get dirty, bend, corrode etc.
The GEN2 bulb is part of a 24v circuit. Here is the path:
(You have read the first few pages of the troubleshooting section of the TM 9-2320-289-20 manual haven't you? This tells you how to read the wiring diagrams.)
1 - Power from the 24v fuse thru the orange wire .8 ORN-922 to the connector plug for the instrument cluster
2 - From the connector plug, thru the circuit board to the bulb and back to the connector
3 - From the connector to the GEN2 relay at the center of the dash. It is mounted to the plate along with the Voltmeter Relay and the Starter relay. The wire brown with a red stripe. 1 BRN/RED-920
4 - When the key is on, the relay is energized and aloows current to flow from the relay to the GEN2 Diode at the top of the dash via the brown wire 1 BRN-25Z
5 - From the diode current flow to the firewall connector via the other brown wire
6 - From the other half of the firewall connector current flows from the connector to the GEN2 via the brown wire 1 BRN-25Z (sxl)
So there are alot of things to check. Start with the fuse, then the bulb and socket, the circuit board (many times it has a bad copper connector), the relay, the diode and of course the wiring itself.
Another problem area is the firewall connector. GM used some type of grease during assembly. With 25+ years of heat, cold, neglect, the grease has turned into a tar like substance. Sometimes it will interfer with electrical flow. A good cleaning may be inorder.