They make those aftermarket switches for the CX500C and I was wondering if that replaced that whole red wire and box. There is no spot for a fuse on the box In the picture I provided. I wonder if that wire off the box runs to the fuse box. Thanks for help I appreciate it, I will have to do some more research.An after market solenoid may have the fuse built in as part of the unit. This one for example. https://www.amazon.com/Starter-Solenoid-Silver-1981-1982-1983-1986/dp/B06Y2GR19K
I have no experience with this particular unit, it just showed up in a web search.