The accelerator pedal that was serviced through Ford at least since the late 1970s came with the SS trim installed. I'm guessing that explains why it is seen on lots of cars.
Otherwise, I believe all '65 and '66 GT350s originally had pedals (brake, clutch, and accelerator) without the trim.
The recess in the pedals for the trim is another issue that the OP did not ask, but I have seen the brake and clutch pedal pads without recessses originally in cars up through the carryovers. I've also seen the later pedals with the recess that are believed to be original in many carryovers. It appears that, with most everything, there was no distinct transition from one style to another. It's worth noting that the accelerator pedal without the recess seemed to have been used on only earlier cars in '65, and you will find the ones with the recess originally used much earlier than the other pedal pads.