Thanks for the replies. My car was a CA car with A.I.R. in it, originally. The cable definitely didn't look home made. Looked very professionally constructed by somebody.
I only had the cable on one side. It looked exactly like the cable on the right side in this pic and was looped into place exactly like the instructions in the background in the bottom left (around the manifold and through the engine mount) -- the second cable and bracket were not present:
Then, based on people's notes above regarding a recall, I found this brief excerpt online:
Report Date: December 29, 1971
Campaign Number: 71V235000
Component: ENGINE AND ENGINE COOLING:ENGINE
Summary: THERE IS A POSSIBILITY THAT A SEPARATED MOTOR MOUNT MAY ALLOW THE ENGINE TO LIFT, WHICH MAY AFFECT THE THROTTLE LINKAGE, MOMENTARILY INCREASING THROTTLE, POSSIBLY TO FULL THROTTLE.
Consequence Summary: UNEXPECTED LOSS OF THROTTLE CONTROL MAY CAUSE LOSS OFVEHICLE CONTROL AND AN ACCIDENT.
Corrective Summary: INSPECT ENGINE MOUNTS AND INSTALL RESTRAINTS WHICH WILL LIMIT ENGINE LIFT AND ELIMINATE POSSIBLE SECONDARY EFFECTS TO THE THROTTLE LINKAGE DUE TO ENGINE MOUNT SEPARATION.
Indeed, the motor mount on the driver side (opposite where my cable was located) was separated ... for how many decades, who knows!
[...]
And I found this old thread with a lot more information, including the original recall letter from GM. I originally posted this when I was busy removing the engine. I'm now sitting down and have time to research this further. Very interesting stuff. I still don't understand why I only had one cable, instead of the two prescribed by the recall. But, I definitely need some new engine-side motor mounts!!
https://www.camaros.net/threads/gm-motor-mount-recall-1967-69.170417/