Chuck,
That's exactly where the transfer switch is located. In addition, the transfer switch has a short time-delay after the generator starts--so it activates a few seconds later. I think the combination of your symptoms definitely points to the transfer switch. What type of "vibration" do you notice? First thought would be that the relay that pulls in to transfer power from the generator is not pulling in cleanly with one "click", but is vibrating back and forth. It's about the only moveable, mechanical, thing in the transfer switch.
You can access the transfer switch by locating the two long screws in the face of the vertical carpeted panel and removing them (you'll have to dig around in the carpet and feel for them to find them). The panel will come off; the transfer switch is behind that.
Mike
