Bad alternator or charge diode.
However, until you've had the battery charged & LOAD tested are you sure it's NOT the battery?
A 3 AMP charge system simply won't keep up with a bad battery.

Green charge light not on. No change in battery voltage, engine on or off. New battery.
So it has a 3 amp non regulated diode system ?

I probably spoke too soon-

Look for a "lump" in the wire that encloses the diode(s).
There could be 1 or 2.
OR
Possibly you do have a 5 or 9 amp system. IF so, the wire would go into a Voltage Regulator.

What's the color of the wire & connector?
Does it feed into a small "box, split into 2 separate wires or???

There are some other systems that have their specific color codes of wire/connectors.

You were right the first time, 3 amp non regulated diode system.
It is working, it is a marginal system.
The reason the charge light didn't show charge, bulb burned out.
After your post I went to the Briggs site, I got into there electrical systems. The 3 amp was shown and all the others.
Going to give the new battery a good charge and go from there.
Thanks for your replies.