Battery Charging Issues BS 42A707

On a Craftsman 917.258570 42 Inch cut lawn mower. I measured the voltage at the battery, engine off, 12.56V. Started engine, ran for about ten mins and check the voltage again with engine running, 12.56V. Ammeter just sort of jiggles near zero. The battery is a couple of years old, sat through a freezing winter etc. Although water levels are good the battery may not be. Could a not-so-great battery cause the reading I am getting? I don't think this engine has a voltage regulator, just a diode which I can't find. Wires coming out from under the flywheel seem OK. Any other way to verify if the alternator is actually working? The lights work and do vary in brightness as the engine speed changes as is described in the owners manual.
Thanks for any and all input.

 

Were you testing running voltage at wide open throttle position ?

A not so good battery could pull what voltage the stator puts out and give a lower than normal reading.....

Would need the color of the wires and wire connector plug on the stator to identify which one you have for proper testing.

 

Yup, wide open throttle. I'm looking for the wires you mentioned. I'm going to buy a new battery first and see what kind of readings I get. I forgot to remove it last winter and would guess a stint at 10 below would more or less ruin it.