Your alternator is not wired correctly if it has an extra wire cobbed in to give 12V to the #1 terminal. That terminal does not need voltage input for the alternator to operate properly. Terminal #2 is the sensing terminal. It needs input voltage to start the alternator charging.
As explained above, #1 terminal operates the light. When you turn on the key, 12V is sent to the light circuit and it finds a ground in the alternator. When the alternator is charging there is 12V at terminal #1. Therefore, the light can find no ground and can not light.
Also you state it is wired just like the diagram Bartamos linked to above. That diagram is for conversion from an externally regulated alternator to an internally regulated one. If your truck originally had a generator it will not have the plug shown in that diagram and can't be wired that way.
I'd suggest that whoever wired this had no idea what he was doing. I'd also suggest finding someone who does know what he's doing to re-wire it.
