I can take it out and run it on another battery, but when I plug it into the harness, I get nothing.

 

I dont know how the rodeos are but i had that happen on my dakota and it turned out to be a plug that went to a relay that was going into the firewall . So i took it out (was riveted in but replaced with screws) and saw that it had been burnt out on the inside. so soldered the points back together with a piece of wire and the blower worked like a charm. I'm sure you could buy a new one though. might be something for u to look into.

Have you looked at the fuse?

 

Yes. Fuses and relays.

 

actually I PROMISE you that its your blower fan resistor look to the left where the blower motor mounts its just a single thing with two philips holding it together the solder releases after the years and you can just resolder it.