Some more mud for the water....

if you do decide to wire in the temp ign light circuit as described.... Might be worth giving the original ign light wire now removed from it`s connection to the alternator, a definite good earth anywhere that is handy, and watching how the original ign light performs while you are also monitoring your temporary ign light set-up with the engine running...? Of course the original ign light should then be constantly lit with the ign switched on whether the engine is running or not , and if seemingly intermittent in terms of it`s brilliance then perhaps indicates the fault is within it`s interconnections with the ign switched side of the circuitry and not in the alternator...?

Worth a try... ?