Wht size is the seatpost? SX1000 had the same seat-tube that they ended up using in the Sting, and took a 26.8mm seatpost. The others were regular 13/16" posts. I have a Scrambler in my basement that takes a caliper rim brake...i'm pretty sure it was originally a 36/36. FWIW, even '79 36/6 frames took a rim brake...
Looking at your bike, it's in the silver color paint, which was available on the SX100, SX500, and SX1000-- but NOT the 36/36. Your forks are the style used on the SX100 and SX500, not the hotter jawns from the SX1000.... but, a lot of parts can be swapped over 38 years, so I'd see what the seatpost is.... the SX1000 had full chromoly frame, and used different tubing. That's going to be your most reliable identifying characteristic.... and, being that the wheels and most of the other components are gone anyway, it's the only one that really matters.