The dimming could be the regulator/rectifier transiently failing, which can explain failure to charge.
Put a fully charged battery in and start it, rev to 1800 to 2000 rpm and verify that voltage is at least 14 volts at the battery. You might see transient drops (coincident with lights dimming).
Now disconnect the battery (positive side only is OK. What voltage do you read from the battery? Should be 13 volts or more on a charged battery. Now, see if reconnecting it causes that voltage to drop (ignition turned OFF). There should be no change in voltage. If it does drop, at all, something is drawing current. If so, you may be able to isolate whatever it is by disconnecting things one by one bus connectors like headlight, turn signals, starter button, etc.
If there is no drop in voltage though, you might just have a failing rectifier/regulator (maybe $25). Or, the stator could be failing. The stator is connected to the rectifier and it is the big round thing on the crankshaft. Wires should come out of the engine case somewhere. It should generate maybe 30 to 40 volts AC when the engine is running. The rectifier/regulator has a diode to change it to DC output, maybe 14.5 volts when running 1500 to 2000 rpm.
Check these things out, and you may discover why you have transient dimming, and battery is discharging.
Good luck!