have pulleys on my car, finally put a belt on it and hooked up the Alternator, The battery Light is on and even when holding a higher RPM it doesnt go out?

Is it a gaurentee that the BBK U/D on the alternator pulley is the issue, or would a new Alternator be the option? my current Alt history is unknown, its was dirtier then shit and i cleaned it up. Never tried it before now, its been sitting for 2 years.?

i just dont wanna buy a new alt if its just a pulley issue? Seems kinda dumb that BBK will sell something that causes charging issues.

Car has NO/AC or big stero either. I can try the old pulley but i thought i'd ask here first.