I have an old Troy Bilt Horse tiller, model 12090 with a 8hp Briggs Industrial Plus 196437, type 013401, code 9612181A. I bought a direct replacement engine, Briggs 19N137-0084 (https://www.smallenginewarehouse.com/19N137-0084). I have a question about wiring: the engine is electric start, but came without the starter switch. It has 2 wires hanging out, red and black (see picture), one male, one female. Manual doesn't explain what they are and I can't see where they end. I think red is battery charging wire, black is engine ground. I have a wiring diagram from the parts manual for my tiller (second pic).
I was planning just wiring it up exactly like the diagram shows, except now the solenoid is on the engine itself, so the red wire I'd just loop back to the solenoid terminal, the black wire I was planning on connecting to the starter switch ground. Is this correct? Thank you