I've read a whole bunch of posts about this issue, but none quite seem to answer my exact issue.

About a month ago, I had a short in fuse 16. I ran a new wire from the shifter light (where the short was) up to the rheostat, but since then I have had to lights in my instrument panel. I was fussing around with it today and checked plug in 10 on connector 31 (Brown wire from the rheostat to the instrument cluster) and my ohm meter gave me the dreaded short buzz. I checked all the other plugs, 10 was the only problem.

So how do I fix a short in plug 10 on connector 31? Can I take the wire out of the connector? If so how?

--Update--
So I have lights again since plugging everything back in. There was a harsh bend where the wire went into the connector, so my best guess is that the wire is busted inside, but when it sits the right way, tada, it works and I have light. Any other ideas of what it could be or is this my best bet?

 

Sounds like you have the right--a break in the wire. I don't know of any way to removed the wire from connector 31.

 

to confirm its a broken wire at that bend, I believe I'd turn the associated light on, and wiggle the wire, see if the light blinks. if it does, I'd probably cut the wire at the kink where it appears to be broken and splice it, either with a waterproof (marine) crimp, or solder + shrinktube.

I dunno specifically about those instrument panel connectors, but most connectors, the contact inside the shell is inserted from the back, and 'snaps' into place courtesy of a tab sticking out of the pin. a very thin small screwdriver can usually be used to depress this tab so the wire+contact will come back out. then before reinstalling, use said tiny screwdriver (like a watch/eyeglass sized flat blade) to gently pry that tab back out far enough that it catches whatever holds it in place when its inserted back into the shell.

I don't know which pin type this particular connector uses, but here's ALL of them...
Volvo Cables, cable terminals, sleeves, and seals

 

Thank you both. I'll try jiggling the wire to confirm the break in the wire. I can't splice a new wire in because the suspected break is right outside of the connector, so there's no room to splice. Hopefully I can find the matching connector and get it out to replace the wire in question.
I'll post another update once I have tried all that out.