1) I will in no way guarantee it's a bad connection, but bad connections are often temperature dependent. The metal expands and contracts with temperature, and a bad connection might only be prevalent within a certain temperature range, such as what you might see four to five minutes after engine start. Again, it may not be the problem, but there is a reason why it might only occur at certain times. And please remember, although no one else is guaranteeing a wiring issue, they've seen wiring problems cause such symptoms many times before. That's why they're recommending it as a likely cause.
2) Not sure how you'd be able to do that with the engine running for several minutes. But since I have no personal experience in that regard, maybe someone else has a good idea.