Ok, thanks to all for the help. Here's where I am with the situation. I went down to the trusty Napa store and bought a new relay. I checked the wiring and it checked out fine. I installed the new relay this moring, and so far so good.
I have the old relay still, and was thinking that I would cut the darn thing open with my Dremel to look for burn spots. That is unless one of you can suggest a way to check it with a meter or continuity light. I'm open to anything.
To Stevesr and Horvath. I should of put more information in my original post, sorry. It's a 1970 C-10-350 Fleetside. The truck sat out under the pine trees for about 18 months just before I bought it. The windshield leaked some, and things under the dash (and elsewhere) were corroded, so I guess weird stuff can be expected. If it happens again though, exorsism just might be my best option.

Thanks again!!