Aaron -

I am a 240 guy, but there may some helpful similarity. The alt light comes on when there is battery power to the light and the other side is grounded through the alt brushes/rotor. So, if the alternator is charging, no light, when it's not, yes light, whether or not the rotor is spinning.

When you turn off the ign switch the small voltage required for the alternator to create electricity is gone, no charging, yes light.

In your position I would check the alternator brushes. Easy to do, disconnect negative bat cable, pull brush unit from back of alternator, takes a small flat tip screwdriver. Brushes min is 3mm. A used but better unit from practically any 240/740 1981 to 1993 should fit OK. Or, buy brushes and replace them, Or buy a new brushes/regulator unit (more bux) and replace the whole unit.

Good Luck,

Bob