Yes I think you are going in the right direction.
I am assuming you used a meter scale that was higher than 5,000 ohms to check it. Otherwise it will read as open (20K on most digital meters).
No you cannot short it out!!!
It is there to drop the 240 heater voltage down to 120 volts for the timer motor.
It looks like the part includes 2 female connectors so you can replace the male connectors with these if required.