It could be something as embarassingly simple as a loose alternator belt.

Possible. Given the way the Miata belts are tightened, I doubt it, though. I'll check it to make sure, however. It is getting slightly better each day, so I think battery charge playes quite a big role in this.

But back to the original problem (the Majestic amp generating a voltage on the remote turn-on lead): Is it possible that a remote turn-on lead routed right next to the constant power wire could induce the increasing voltage? Or is the amp necessarily faulty? The amp does produce some noise (low level hum), but it's a cheap one and I never expected it to be perfect.