Your first picture seems to show a normal speed control linkage, with the cable missing. The bracket that holds the cable outer is there, and the bell crank that connects the cable inner to the governor spring. The mechanism is the same as on your I/C Quantum engine. On the John Deere there is something that looks like wear marks on the paint on the bell crank where the cable would attach. Are there any signs of a screw having been in the screw-hole for the cable anchor, to the right of the speed control bell crank?
Does your John Deere dealer say it is not supposed to have a speed control?
Personally I'd be reluctant to buy a mower without an engine speed control. I only use maximum engine speed in tall/heavy grass, which I don't usually encounter except for two mows each spring. The rest of the time I'm running well under maximum speed - maybe 2,500 rpm, where maximum is 3,500.
