Re: starter engages while driving
That part about the tach swinging wildly at the same time makes me think about the HEI doing something it isn't supposed to do.
That being said, I was having starter jitters when hot and I assumed it was the old heat soak issue. I had to install the lower bell housing shield last month as my car came without one. A friend came over to help and said "let me take the starter to a buddy who does this stuff and see what he says".
The starter came back with a new bushing in the pinion side of things and a new solenoind. It has been hotter than Hades here lately and the starter is working just great. My point here is maybe pull the starter and have it gone thru by a starter guy and see what's doing. The cost is quite minimal. If the pinion bushing is worn out, that could cause the starter to hang. Granted, it doesn't answer why it engaged on it's own but it is a start. (sorry, sometimes I just can't help myself).
Also, if the starter is engaging no matter what, disconnect the cables from the starter, keep them well out of the way of any grounds and hook up a DVM, one lead to the purple wire, one to ground. If you reconnect the battery and the DVM shows 12V with the key out, you have a switch issue. It should read 0 V with the key out.