I can't add much to the wiring problem, but I can't see that being the cause of your first problem. Electrical problems tend to be on or off, and if they're intermittant, they're constantly intermittant (if that makes sense).
I've seen a similar problem to your fuel issues. More than likely your fuel tank has a "tap" that has a vacuum activation, i.e. a small hose from the valve to the intake manifold. I saw this on an old VFR400, which would run for about 15 mins, then die. Once you left it for an hour or so, it would start again, only to stop about 15 mins later again. The fuel tap had 2 identical "nipples" which the manifold vacuum hose would fit on. One was the right one, the other was just a breather. Any guesses which this one was on? The reason it would start is that fuel was leaking past the tap and filling the fuel bowls, but would cut out after the bowls emptied.
If your bike's injected, disregard all of the above, check power to fuel pump when hot!