I'm thinking it may be the generator itself. I have continuity on both sides of the generator wires. When I do a peak voltage test,I only see a few mV like you said. I'm doing this with a multi meter set to peak mode. The manual says I should see at least 3.0V though?
Are you using something like this? (I don't know if this is the right kind but they do exist).
https://www.amazon.com/CDI-Electronics-Voltage-Adapter-511-9773/dp/B001O4TZGG
I don't think a multi-meter can measure the peak voltage directly, its too fast.