+2 on checking how the solenoid was wired. It could also be a bad battery cable(s), battery terminal(s), and/or just some wiring issue(s).
It's pretty common to have a bad battery cable or two on older SHOs due to corrosion inside. What happens is the strands break off on the inside, and then when you jiggle around the cable(s) just right, the broken strands "reconnect" again. I've replaced all cables on both of my '89's, and now they don't give me any electrical issues.
Make sure the smaller wire from negative terminal is grounded on sheet metal off to the side of battery, and smaller wire from pos terminal is connected. Or, it won't start as simple as it might sound, since they are for your ECU. I'd look into the cables, wiring connections, and to go from there. Good luck!