I can't seem to get my passenger tail light to work. It was on for a bit last night while driving, but for the most part has been out for the past 2 months. The side marker in the back is out too

I hooked up a multimeter and I'm getting current. Bulbs are new. Is there something basic I'm missing?

 

You are getting current. But how many volts? Corrosion of the connectors (harness and bulb socket) leads to higher resistance and the tail lights like something close to 12 volts.

 

I'm getting a solid 10 volts.

 

11+ volts would be better. Have you checked the voltage directly at the bulb sockets? Both the ones that work and those that don't (for comparative purposes.)

I went through this drill last weekend on my '89. The terminals IN the sockets were green with corrosion.

 

I'll check the other side tomorrow. Good idea to compare. What happens next if I can't get the voltage above 10 ? Bumper removal time?

 

Check the ground point behind the rear panel on the pass side, near tool cover. I had the same problem, my pass tail light would work sometimes, other times not. I pulled back the corner of the rear panel and found a heavily corroded ground post. I cleaned it up with a wire brush on my dremel and it works good as new!

 

I had the same problem, in my case it was the lamp control unit (bulb tester) -> see the recent thread 'Tail lamp warning?'