On my 2000 fxds, I had a similar problem, went thru two stators and 3 voltage regulators,,, Many batteries on that bike... Over 117,000 miles though
Something you might want to checked or get checked,,,
I have found where the "Stator electrical connection" between the stator and where it connects in-front of the motor,,, Inside the Rubber Boot,,,, That when changing oil and filter Some Time,,, It got Filled with oil....
You might check that plug,,, or have it checked to see if it is filled with the old oil.... That can't be good for the stator and May cause a future problem...
My stator started out by the light going on then later the SMELL of Burnt was detected... Taking off the Derby cover or the chain adjuster cover and WOW,,, Burnt smell Strong!
Now that was just mine,,, I do attribute the OIL in the Connectors(filled) as a possible problem but not sure.
Just another place to check.. Seemed ALL the 2000 TC models had the same type of Stator connector and Location was on the front of the motor,,, Where the Boot N Plug are Under the oil filter area an easy to get oil inside when normal service is done....
The stator cost about 250$ labor about 300$ and the voltage regulator about 125$ and 40$$ to install.... Giving you those figures just as Guide-Lines IF you need to get anything replaced by HD..
signed....BUBBIE