Self-cranking starter

I had electrical problems a few weeks agao, where my 1999 Saturn SW2 would intermittently and suddenly stop (or not start). It would not crank or make any noise when the key was turned. The dome light, radio, doorlocks, and warning bells would not work. The headlights and windows would. The battery was fine (and well-connected), and jump-starting it did nothing. I messed around with it for a while, and found info on the web about loose/hot connections in the fuse block at F5. I inspected this terminal, and it looked a bit overheated, so I tightened and cleaned it and reinstalled it with dielectric grease (which I intended to disperse the heat?). Now the car starts and runs OK, but mysteriously cranks for a second or two every now and then when it is sitting in the drive overnight. There is no key in the ignition, and it seems to happen at random intervals. It does not sound like it is getting any gas, it just “dry-cranks.” Is there a mechanical/electrical explanation for this (and a “fix”), or is the car possessed?!?

Primary suspect: ignition switch