I thought I should explain how I arrived at the circuit I am using. These batteries are very sensitive to over charging. In the original IBM battery pack for a laptop, it has a computer chip that senses the charge current, voltage, and temperature of the batteries. Way overkill for a bicycle. I know from experience that 40 ma (max) long-term will not harm my battery pack, so that was the target for a fully charged condition.
When the battery is low, and/or the lights are on, the current across my 120 ohm resistor can go to .12 amps. More than sufficient for my needs.
I had previously rejected zener shunt type regulation, and a LDO (low drop out) IC (integrated circuit) type regulator because they both use considerable power to operate, and with only 3.5 watts to play with, a simple but carefully chosen resistor value was the easy way to go. The simplest things work the best.
There is no capacitor in my completed circuit; the battery does not care if it is only half wave rectification, and smooths it to prevent headlight flicker at idle.
Sorry, I did not mean to get long winded, and have no desire to become the Motoredbike forum's electrical guru.
-Flap-