My son bought a 1987 2 wheel drive 4 cly. the lights did not work he replaced a fuse and several lights they worked fine untill he drove it about 10 miles and then the lights quit again. he drove it home the battey post became loose and it quit. he replaced the battery and it will not start. there is a small wire that he found broken that comes of the pos off the battery he conected it and sparks flew. HELP when he try to start it you can smell an hot electrical smell in the cab.

It seems to me you want to follow that broken wire to find out where is goes, on the hope it powers the lights?
When you have a short circuit like this, The easiest way to do it is to put an oscillating pulse down it, and then trace for it with a signal receiver and speaker. Harbor freight sells the pair for tracing phone lines, for under $50. You could make your own with a flasher to generate, and an inductive ammeter, galvanometer, or a coil and speaker. Or you could just assume it has to go to the fuse block, ignition switch or something big and important, so you could look until you found what used that size and color wire. Of you could let it get hot and feel the heat or wait til it shrivels and use that to identify it. But it is probably cut through its insulation where it goes through the firewall. Although I had one car where the accelerator cable sawed through the wire harness.