The '68 ST300 down shift switch is absolutely found at the back of the carburetor on the driver side. The circuit gets power from a black wire with double yellow stripes that goes to the windshield washer solenoid where it shares the same terminal as a black wire with a single yellow stripe. The opposite side of the down shift switch has a black wire that goes directly to the down shift solenoid on the driver's side of the tranny.
Give up the argument on the switch at the pedal. It just ain't so on the FGF.