On my 88 there is a black box that connects into the wiper circuit and then out to the wiper motor. Sounds like what you're looking at...probably fried it and needs replacing...they are usually just a printed circuit with a few doodads for the various speeds so not likely something you could tear down and replace parts on...but might be worthwhile...
I have a 96 that I've been taking the dash apart and I think I saw this up where the glove box opening is...but I'm still checking everything out so not sure...
But on my 88 there is a way to disconnect the box so likely an easy replacement...if you can get at it...
If you don't have passenger air bags that cover on the dash is easy to pop out and have a look around...if you have air bags...make sure you disconnect the battery before poking around in there.
EDIT: I just checked the on-line manual and after 95 (so yours is excluded) these trucks used a GEM for a wide variety of functions...including the wipers...so you must have the older style.
If you want to read up on where this is you can try the on-line manual and just follow the steps...
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