(Guessing that my 85 380SE is similar) The trip reset is a rod/plunger type of setup that sits above the rheostat switch. The same rod engages the switch and allows it to be turned clockwise/counterclockwise to vary the resistance in the circuit feeding the light bulbs. The thing is very touchy and can cut off the power easily, for reasons like the mechanical linkage wearing out, or corrosion in the rheostat (potentiometer) wire/contact.
I've had my instrument cluster lights go out when the bulb contacts inexplicably fail to pass enough current to the 2 bulbs. I spent hours pulling the cluster and the rheostat switch, trying to find the failure. In the end, I wiggled the bulb holders in their sockets and that did the trick.
In your case, since the entire light circuit is out, wiggle the rheostat/trip reset button and I think you'll find the problem there. A permanent solution is to pull the cluster and remove the rheostat switch entirely, then jump-wire the 2 contact pins together, effectively sending all power to the lights (which certainly will not 'blind' you with their intensity!)
