Today I've played a little with the setup. I get rid of the transistor and what I've noticed is that I need to power the signal generator with a lower voltage, i.e. to use a step down transformer (a buck transformer) because it draws a lot of current from Battery 1. When the voltage that powers the signal generator is around 2VDC the other two batteries are charging. But is not my definitive word on that. I will test further.
For those that didn't know what the setup is, it is about this: https://youtu.be/_FpRrJWYbYY?si=HWAnfCRwZPUMAK8c
For those that didn't know what the setup is, it is about this: https://youtu.be/_FpRrJWYbYY?si=HWAnfCRwZPUMAK8c