Percolation? Heat soak? Don't drive during summer??

Rusty,what makes you think he needs a coil? Ima thinking you need more sleep.
I mean OP could practically weld with the one he's got. I have never seen that behavior but coil would not be on my list of things to change, nor would an amp. I'd be looking into what could be telling the amp to fire like that, and of course I would be disconnecting the tach pronto, as others have suggested.

Since the engine starts and runs normally, Ima thinking the amp is being triggered by something else.

Well for one, they're cheap. Secondly, if that thing is charging like that when it's not supposed to, that's taking a lot of life out of it, even if it still "works". Call it a preemptive strike. I realize "something else" is probably causing it, sure, but it's gotta be taking its toll on the coil. So since they don't break the bank, my advice it throw it in the ditch.