battery light never goes off

my wife's 99 neon sohc automatic had the battery light come on about a year ago i changed the alternator and the light was still on i inspected the wiring to the alternator\ battery ect i put a volt meter on it and it charges 13.6 at an idle
so why is the light still on? this is annoying because the belt broke the other day and she had no idea it wasn't charging

any codes?? does you car have a battery temp sensor??

batt temp sensor possibly.

yeah it is broken too the car was wrecked when we got it but the battery light came on after we had it for a while (batt temp sensor was broken when we got it) figured it was unrelated to the batt light since there is a code for it