Before you go too far, replace the stop light bulbs with fresh Osram or equivalent bulbs. I read in another thread that the cruise system grounds through that circuit, and evev though domestic bulbs fit and light up when you hit the pedal, they could, according to that thread, cause malfunction and even damage to the amp.
Just replaced my cruise amp with a used one on Saturday, you're right about the bolt
and full time acceleration went away, but cruise was still not right. Replaced the bulbs (which I meant to do before test drive but forgot), and the cruise now seems to work almost perfectly. Tail light bulbs were OEM, but there was corrosion at the filament so I did those also. Worth a shot.