Does the governor move with the throttle? If you move one does the other
move with it?

The governor itself is deep inside the engine but the lever on the outside (just behind the air cleaner) is connected with a bent wire rod to the throttle valve. Yes, if I move one the other naturally moves. But there is no motion on its own. There is also a second wire rod which parallels the first and connects to a spring which then connects to a tab that is held by one of the carb to intake tube bolts. One bends the tab to adjust the run speed.

Previously, Tec carbs had an upper plate with a lever to adjust between tortoise and hare speed and the back end of that lever attached to the aforementioned spring. It's been dumbed down since then. But the intake tube casting still has two uprights that used to hold that upper plate. Just no longer drilled and tapped.