Picked up this cool little Forest Gump style mower yesterday. 8hp B&S engine (must be old, it's white)

Pull start works fine, but key just causes solenoid to click. I'm charging the battery now; might be the easy fix. Any other suggestions?

I noticed a wire hanging between the battery and engine, and there is no obvious point for it to connect. The wire is bolted to another wire that goes toward the spark plug. The bolted connection has a square, metal, u-shaped thing that kinda looks like a dual spade connector (l_l, bolts and wires would be on bottom of "u" thing). Where is this supposed to go? Pretty sure it's not supposed to just be floating in space.

EDIT:
Oh yeah. The wire comes from the solenoid compartment, crosses to the location b/w battery and engine, then goes into engine toward spark plug. Not sure where it terminates (haven't opened up that far yet). One of the spade looking ends is partially covered in plastic. hard to tell, but looks like the other one used to be. Prob not an electrical connector. Just an old wire clip?

 

Just guessing that it sounds like the kill wire and it should connect to a nut on the throttle control plate on the side of the engine.