TBH my S1 RST on its original alternator (56Amp) will had the alt light dim with all of the consumers on, but very dimly, almost unnoticeable. Maybe I am being soft on the car but I would expect that. FFS my Triumph Stag with nowhere near as many consumers had a 50Ah Alt on it which could just about feed everything! It's fuelling system certainly only required a fraction of the current!
I reckon that ditching the kill switch should help matters but in your case I would check the battery voltage and the earths. IME pattern alternators in Escorts never lasted any length on time. This is where a 6 month old alternator once landed me...
OTOH the Italian company was quite something!