Unregulated, the Model A generator can put out up to 32 volts. Tied to a battery you might get 7-1/2 volts.
Many use a voltage regulator adaptation. This to get past the Model A era issue of "boiling off the electrolyte" which can happen as a lead-acid battery is "overcharged."
Prominent in the Model A Instruction Book is the instruction "frequently check and add to your battery cell electrolyte."
In the case of your alternator, a voltage regulator is probably included - the system NEEDS to be regulated lest you burn out your alternator.
I'm suspicious that there is something in your system regulation that is differentiating between just the battery being charged, and other components of the system added. It could very well be the battery itself, especially if you're using the AGM style battery - which historically are less tolerant of "out of design" condition.
An AGM battery once it has been frozen, even if it is thawed out, becomes a very "small" battery in comparison with its former self. And yet it will show proper voltage.
Load test will tell you more.
Joe K