Steering Column Swap

I'm frankly astonished that differences in the PATS plug was all that you found.

To make PATS work, is it possible to remove the transceiver from the 96 column and put into the 03? Obviously some re-wiring would be needed.

To disable PATS in a 96+ model year Mustang there isn't a magic wire to cut that will make it happen. For most people the best answer is to disable PATS with a custom PCM tune.