Working on my '85 GMC S15

I have an '85 GMC S15 2.8L with a 2 Barrel Carb, rear wheel drive with 94,115 miles on it (which probably rolled over before I even got it). It has the original engine it. I've replaced almost everything on it, but i've also come across problems with it too.

i was having probs starting it, and so I switch out the starter with a new one. I've also changed the battery with a brand new one (with a warantee this time). But I was still having probs getting it started. I asked people at work and they would tell me to check all my grounds, which I did.

i eventually got it started by jumping the starter (it has the 'S' type starter), by touching the contacts. (Is prolong starting it this way harmful to the starter by the way?). Anyways, after two days of starting it this way, I noticed a smell of something burning, so I check the engine and couldn't find anything.

so, I started it again, and again I smelt something burning. So I decided to check up underneath the dash, and I found this wiring attached to the top of the steering column under the dash.

after trial and error, I found that one of the wires would keep the starter going even after jumping the starter off, and the other wire had to be plugged in for anything to work on the dash, or for the starter to stay running (i accidently found this out by looking in there and kinda probing and moving around with a phillips head screwdriver, when I came into contact with both wires and gave one heck of a shock and sparks, then the truck started up).

by the way, the thing that the wires were plugged into was melted. And i've tried to find out what it's called so that I could possibly get another one. And does anyone know if this would help solve my grief.