When it shuts off,it will not start right back up,right?you need to have a volt meter with you and probe the purple wire(its the run wire from the key swittch)
you'll have to work quickly. Good luck these problems such to find

It will not start right back up.

I ordered another alternator. I'm hoping that it's just charging too much.

15.5 volt if I remember correctly ?

where were you seeing this on the amp gauge ? if that correct its to high....should be around 12.8 - 13.2 ? could be over heating a component and failing till it cools off

With the engine running / charging check the voltage at the battery ....see if the auto parts place can test it before you install it

Yes on gauge. (Volt gauge actually)

so no start period ??? If that is the case

test the pick up coil in the distributor -- possible your issue if so buy the merc one -- read the post 502 will not start