Take a multi and test for voltage drop at the alt, reg, ecu and across the battery terminals. Check for variations. I've had similar issues and it was a weak regulator. As mentioned are you sure it's I thermally regulated?
12 volts boarder line. It will weaken your battery Forsure eventually. Mine comes up some when you rev. But it should spike either. 13-14.4 volts is pretty good stable reading. Any higher and your gonna cook your battery eventually. Any lower and you'll kill it eventually.
Does it drop a lot when you turn On The lights and /or A/C etc? Something else to check....maybe you have a lot of accessories that are putting a bigger load on the system than it was designed for? Just questions....
Good luck let us know what you find
