my rear defroster blows the fuse when activated. I have ruled out having a short at the door hinge area and believe that I have a faulty relay which is hardwired into the fusebox.

I want to run a power wire to an aftermarket switch then back to the rear glass. How many amps should that be? If the original setup used a relay then its gotta be at least 40 but the original pink brown wire is too small for that.

 

The original setup used a relay (and is fused with a 30 amp fuse) because the rear defroster and heated mirrors are all controlled using the same switch, have you investigated the mirrors as a possible location for a short? Otherwise take a voltmeter and measure the resistance from one side of the defrost grid to the other at the unplugged terminals. Once you know the resistance divide 12 by your measured resistance value to get the nominal current in amps.