So I finally had time this WE to start my Beta after 3,5 month of inactivity, it started right up and I measured the voltages:
https://www.youtube.com/watch?v=jYG5hEAbgNAIt started at 13.13V with the engine OFF, then tropped just below 13 for a few seconds and stabilized around 13,10V with the FAN OFF and around 13V with the FAN ON.
So I would say in your case you have an issue somewhere, most probably the voltage regulator.
Ref: 11
27.28101.000RECTIFIER, ENGINE 250/400/450/525 EXC
Price: $100.53
The price is shocking to me honest, If I needed one I would probably try some generic ones or from another brand...
Cheers !