You need to be using a meter, not a light. BUT...
If the alt stud won't light up a light, but the battery is hot, you have a bad battery cable. That red wire you see on the back of the alternator is the same red wire you see hooked to the positive terminal at the battery.
Here's your next test. (it's a two parter)
First, put your test light on the ALT post and then wiggle the crap out of that wire at the battery. If the light blinks on and off, you've found the problem.
Next, jab the light probe into the red wire about an inch from the battery. If it's dead, you found the problem.