Simon;
Again, that is either a highly unusual combination from the factory OR someone's Alternator conversion...so I can't be certain of wiring configuration around the Alt, or even if it is an Alt with External or Internal V Reg.
Only by careful inspection of wiring will you be able to determine this, and this will be necessary to know to proceed with troubleshooting on the vehicle...I expect wiring to resemble that shown on 123GT page (for external V Reg) OR this extract from 1800E (also ext. V Reg,
https://sw-em.com/1800E_Wiring_Diagr...ys_Excerpt.jpg), OR this (generic GM Chg Sys config with internal V Reg,
https://sw-em.com/gm_charging_sys.htm )
I suggest a careful inspection, and recording (including color codes) of what you have and either posting it here or contacting me directly per e-mail (don't use forum messaging!)...some pictures of Alt and Reg wouldn't hurt...of course, you could simply remove the Alt, take it to a elec service shop and have them check it stand-alone...but that is little progress when they tell you "...it works fine!". I recommend testing in situ, which will allow narrowing it down to Alt or VReg.
Good Hunting!