My first thought? Solid-state electronics don't tend to like variable supply voltage. Except for diodes/rectifiers, they really don't like AC voltage.
Got a small alternator shop anywhere close? Not the "big chain" shops - they can't test for this sort of thing (and don't know what you're talking about anyhow...) but a shop that would have a shop 'scope or a real test bench. Last time I saw something like this, I finally tracked it down to alternator ripple - and that has to be checked for with an oscilloscope or a shop 'scope.
Your alternator natively generates AC voltage (makes it mechanically simpler and smaller than the old-style "generators" - and that's why it's called an "alternator.") In the back of the case, there is a diode pack that is used to convert the AC voltage generated inside to DC voltage that can be used outside. While it's not "pure" DC voltage (there's always just a trace of ripple, but you need a good scope to find it...) it's close enough for our purposes.
If the diodes fail, they can fail in one of two ways:
1) "Blow out" - this is the most common. What happens is that the diodes stop conducting electricity at all (normally, they're like one-way valves for electrical current) and you don't get anything out. This is a fairly common alternator failure in general - usually, either the diodes blow out or the brushes wear out and you don't get contact anymore.
2) "Short through." Instead of only conducting electricity in one direction (and working to convert the AC into DC,) they conduct in both directions - letting the AC voltage through. Since the solid-state electronics in the control system are designed for DC voltage, they don't like AC - and typically can melt down as a result.
The more ripple you have, or the more "failed" your diodes are, the faster you'll blow out electronics. Control units are just more sensitive to it - you can eventually blow out your radio and such as well.
The fix? Replace the alternator.
To test? An oscilloscope. Typical "chain store" benches only test for voltage output (at a very low current - but that's been discussed before by me...) and don't display ripple at all. You'll need somebody with a "real" test bench, or someone with an oscilloscope, to find out about ripple (and how bad.)
This just leaps to mind because it's something I've run into before. It's quite rare (I think I've seen it one in the last twenty years or so,) but it can happen. So, it's good to at least rule it out. It just leapt to mind because it's the first thing I'd look for now, having seen it before...
