Before you start it:

First, that connector above is the one I wanted you to inspect to look for any signs of burning/damage
(also - how did the connector the R/R plugged into look?)

Next, at same connector, do the test I outlined earlier - measure the resistance between any of the three pins (does not matter which one) to engine ground - should be 'open' i.e. infinite resistance.

If that is good (i.e. not short) then you can start it;
with meter on AC Volts measure from pins 1-2, 2-3 and 3-1 in turn (doesn't matter which you call 1 etc)
All three should the same at any given rpm - at idle expect ~ 20V. As you increase rpm the voltage should rise, but again, if you fix the rpm (say 4000 rpm), all three should be the same - the absolute numbers are less important, that they are balanced is what indicates one leg is not 'down'.

Again, if you get a 'short' in the first (resistance)test, don't even bother starting it.