I just wired mine back up with the OP's posi-lok system this week so the 4WD light would start working. It is a grounding wire that goes from the bulb in your dash to the blue-ish vacuum switch on your firewall. The wire is black with a yellow stripe (on an 87 at least). There's a yellow one with a black stripe in there too - leave that one be.
I think fishadventure is on the right track though - and I'd lean more towards a chafed wire or dirty contacts making the wire ground out. If it's always on, I doubt it's an issue with the contacts in your dash. Several of them share +12v connections on the flexible PCB board behind the bulbs, but they all have independent ground circuits (as this is how they light up). If it was a short behind there, the 4WD light would only come on when another bulb had good ground (seatbelt, brake, etc.).
Hopefully it's something simple, but a posi-lok kit wouldn't be a bad idea if need be.
1987 YJ Sport, I6 258, Weber 32/36, CRT HEI, RC 4" lift, 33" BFGs, 11.5K Superwinch