As mentioned I believe you have a working rectifier and alternator but not a working regulator
I did look at a manual for later models
https://thexscafedotcom.files.wordpress.com/2011/04/xs650sj-manual-chapter-6.pdf
Not sure if it is the bike you have But it seems as they have a combo where the rectifier and regulator are built in as a unit
Please look if you can se something with a lot of wires entering 6 or 7
There is a test procedure rather long but possible to do
There is mention -->
cheap... but wonder how " cheap "... as in cheaply made.... I'll order one.
I once ordered at combo for an 80 which I have but in Europe with the old system and fried the regulator part inside the combo immediately in the combo
So please give info what is on the bike now
Is it the stock Combo that does not regulate down ( Possibly fried )
Or is it an ordered one as in --
I'll order one.
I went for separate units rectifier and regulator --- has worked for me That stock combo is like a black box ..Even though the rectifier can be ok It inside the black box connects to the regulator in an unknown manner I do believe .
Others chime in if I have missed something here