My heat pump fan outside is cutting on and off constantly when the heat cuts on. We checked the switch outside... could it be a short?

How often is constantly. 2 seconds 5 minutes?

I would say 2 to 5 seconds

Every 2 to 5 seconds would indicate a bad motor to me since that would be real fast control action. You better check to be sure that the compressor in the outside unit is not kicking on and off that fast or you will damage it.