I tried that with a paper towel roll, and it was inconclusive.
I disconnected the primary, thus disabling both the oil pump and tach, started it for a couple seconds, and the noise was still there. While driving it this weekend, I noticed that the buzz stays at a constant frequency regardless of engine speed. It also doesn't make noise when cranking the starter or pulling the recoil. This to me suggests that it's something electrical. The tick of the buzz, if that makes sense, sounds a lot like when I tap the starter housing with a screwdriver.
It does not appear to affect performance at all, so I will keep scratching my head.
Another curiosity, on this machine, is that when it's been running for a while and then is shut down, a few minutes into cooling down, it will make a "pop" sound like those pop guns at Cabela's.