GeoLane at PTD dot NET wrote:
In my case it's an Onan genset with an Onan Elite E140H 14 HP engine.
The generator is a Pro 6000E Model EGHEB

The former owner had alligator clips on the battery cables that he
used to connect to his car battery to start it, and then clamp them to
the frame when not in use. Although that's a dead short, the charging
circuit still works.

That is a Clue!

That's not the problem though. It's putting out 16V, which I suspect
will fry the little U1 battery.

Refer to Clue above. I suspect that the charging circuit is
heavily current - limited and would not supply sufficient
current into the very low impedance of a properly sized battery
to cause harm.

I would borrow a battery from one of my fleet vehicles and
place an ammeter in series, between it and the charging
circuit. Chances are that the current reading is quite
low and that the battery voltage never would get above
a safe level.

--Winston