When I bought my '83 C10 4 years ago, it came with (what looks to be) a Kelsey Hays trailer brake controller. Funny thing is, I don't even have a trailer hitch, and I don't think I'll EVER have need of trailer brakes.
If it is like the one I removed, disconnect the control lever from the steering column. Start following wires; disconnect and remove wires. There is likely a big connector in the rear bumper or near there.