help! intermittent battery light off/on Jetta 2002
 

Hey guys- I'm new here.... yes, I'm a gal that works on my own cars...
2002 Jetta wagon gas.
Just trying to figure out a battery light that will come on and stay on and go off as it pleases. It may stay on for a few moments and then go off and may reappear in seconds or days (sometimes weeks). Been going on/off for about 6 months. When it is "on" it is solid not blinking. This alternator is about 11 months old and replaced from a refab. (The previous refab lasted me about 1 month and failed quickly). It is a bosche and same voltage. Belt was replaced twice in past year, just thinking it may be attributing... Only recently I have noticed a slight dim of lights and heat when it goes on, but nothing like when the previous alt failure was happening. The testing of the battery and alt are showing normal. It starts up fine in negative degree weather.
Only other odd facts that been going on for years and may not at all attribute... driver seat belt light is always illuminated no matter if fastened or not; and car locks automatically (when engine off) if the driver door is not opened... like if you open the rear door only- it will lock down.
Figured I'd get your opinion. Thanks for your help!