You're thinking of 66. 1965 Mustangs were not equipped with emergency flashers.

 

From everything I looked at when I added them to my 65, they were a dealer installed option in 65. Apparently there are at least 2 if not 3 different glove box mounted switches and wiring harnesses. The 65 wiring schematic shows them.

 

conejo172 is probably correct, I have seen a kit where you install a small LED that flashes when your car isn't running so passers-by think it is alarmed.