If that something has been disconnected since you got the bike, and it has been running, if intermittently, that can't be your problem. Unless it's currently dead and that loose wire forms part of your interlock circuit.
If we are down to scrutinizing custom wiring from a previous owner, you may be on your own figuring this one out. Troubleshooting factory issues can often be done successfully with remote help, but once you get off into unknown territory, you really don't know what you have. It's guesswork without hands on.
If you've convinced yourself that the carburetor set up is well, there is no rust being forced through the filter and gunking up your clean carburetors, then turn your attention to the ignition. Look for nice fat blue sparks in every assumption
Also, an assumption is that the bike ran well at some point, or that you did a baseline compression check.