I was thinking too that you may want to verify your car has the correct generator and regulator on it. I don't believe you mentioned the year but if the J is a '51 or a '52 Vagabond, it will have Autolite equipment. If it's a '52-'54 Corsair or Corsair Deluxe, it will have Delco-Remy (there were a very few '52 Corsairs that had Autolite, the serial number range is listed in the factory parts book but it's a very low number).
The Autolite numbers are:
Generator - GDZ-6001E
Regulator - VRP-6001A
Delco-Remy numbers are:
Generator - 1102789
Regulator - 1118731
Check the numbers on them and see.
My '52 Vagabond had a similar problem when I first got it. I was going to install new brushes in the generator to see if that would help and when I removed the generator that's when I found that a previous owner had installed a Hudson generator on it. Electrically the specs were the same but the Hudson unit has a smaller diameter pulley on it so it spun too fast, hence boiling the battery and burning up regulators so be sure you have the correct numbers on yours.
It's easy to forget that some of these cars were restored in the 70s and 80s when we didn't have the internet or forums such as this to find parts and information so you had to make due with what you could find. The previous owner needed a 6 volt generator, found a Hudson unit and installed it. Probably worked fine for a while.
Otherwise, I agree with porsche1914, it probably needs an adjustment.