[Penthode]

I just reread your original post. You indicate that even with no brakes applied, the horn diminishes with just the lights on.

This points to a bad (high resistance) common connection. If the battery ground was bad the generator alone would make the lights too bright.

Is the engine properly grounded? Are the connections to the terminal box good? The highest probability is the ammeter is partially open or the connections to it are bad. (You can check a bad ammeter by shorting together the two terminals on the junction box).

You need the digital meter as it will precisely show where the voltage drop loss occurs. The meter is cheap and will prove very useful.