I doubt its a dead alternator if the electrical is cutting out. If it was the alternator, the battery would continue to run everything until it ran out of juice, which should be about 20-60 minutes (my guess on this, considering the amount of electronic stuff our 4runners have), depending on what battery you have and what you were using electrically during that time.
How exactly was it cutting out? Engine only? Lights? Dash? Everything at once?
Did it just cut out and not come back on again? Or, were you able to re-start it and continue on?
I bet its a loose connection somewhere, but will wait for a bit more info from you to really say. I know this has been covered before, but have no clue what thread it was.