Got the shaker back today. Assembled all the guts (linkage, wires and the two solenoids that are the same as a 69 Camaro cowl induction hood) and it actually works. 1972 was a weird year. Pontiac got smart and instead of using an entire Rube-Goldberg contraption working off the carburetor with a ton of extra parts, they used the existing turbo 400 kickdown switch and worked the solenoids off of that. That is why every '72 Trans Am, regardless of it being a 4-speed or automatic, has a turbo 400 kickdown switch attached to the gas pedal under the dash.
The only problem was adjusting the metal bracket to allow the switch to operate but not restrict full, wide open throttle. That took about an hour of assembly, test, remove, bend, reassemble, test...lather, rinse, repeat. You know the drill.
The switch:
The shaker, installed:
The contraption in action: