Thanks Vic.S! I have some pictures to post. I found 2 black wires on the left side of the motor that were taped up. I untaped them and found one to have an eyelet and the other to have a metal end that looks like a broken eyelet. There's a black cylinder-shaped plug on the left side that will not allow the motor to start if it is plugged in together. Not even with the safety tether plugged in. But having them unplugged seems to disconnect the red kill button on the tiller handle. Also, my fuel pump shape might be that of a motor with electric start if I remember correctly (one is round and one is 5 sided). Anyway, here are some pics...
These 2 wires were taped up and tucked away. I don't know where they are supposed to go or what purpose they serve. Part # 582508 are the ignition coils, as you know.
This red wire runs along the right side with a black wire. The black wire attaches to the right side of the round thing in the middle of the picture (rectifier assembly, supposed to be on electric start models?).
Here you can see where the black wire is attached. I don't know if these are the black and red wires from the front of the motor because they are routed underneath and out of sight once they enter through the engine cover.
The is the black plug (possibly the kill plug) that will only allow the motor to start if the 2 halves are unplugged. Above the plug is a shiny spot that looks like something might have been attached there at one time (the 2 threaded holes).
Any help would be much appreciated, and thanks for taking the time to help me fix this mess.