I have a cb650sc "82} the 81 is the same , you do have an alternator with brushes. mine
needed replacing by 25,000 miles How many miles on the bike?
with the ignition off there should be no drain on the battery.{disconnect one cable,from battery} after fully charging it.
and hook a 12v. test light between them ,see if it lights,
if there is , pull the connecter{s} off the rectifier/ regulator, and see if the
pull{drain} on the battery stops, if so check the diodes{faulty reg.} {see faq's} or
a shop manual on proceedures ,someone here,may have that already up on the
site.
post what you find out.
Hope it helps
Bruce