Christy,
Glad you got the controllers figured out. I hope you're right about the moisture.
The motor boss on the machine head, how many screw holes is in it? I see one. So I'd attach the bracket with the screw through the vertical slot into the hole in the center of the boss on the head. The bracket has a slot to match the boss on the head so that should work.
As for the light going off when you push on the controller, it's wired wrong. That's it in a nut shell. The light has it's own switch, right? Then both light wires should be wired directly to the power cord in the junction block.
The motor is wired with one side to power, (probably the neutral side) and one side through the controller which is the motor switch. Remember the hot side is always switched. There are two separate circuits in that block and they are all connected. Wire them correctly and it works. Wire them incorrectly and you get weird things happening.
~~ Unless the system uses a third ground wire at which time I'm not sure of anything. ~~
Joe