Toro Personal pace mower Auto Choke open at cold start

Sounds like a hybridize engine as it should only one of the choke system or just a primer setup without a choke. Take a closer look at the carburetor either it has two vanes (1 for the choke and 1 for the throttle) or just one. If only one then it is a primer system as the only vane will be throttle control.
 
This engine uses a mechanical governor and can have air vane for auto choking. If has an air vane make sure it spring (small spring) is attached and pulling the air vane toward the flywheel when the engine is not running.

Normally on a cold start it takes 3-5 pumps but priming once the engine is warm to operating it should be necessary but I have seen a few that requires it.
 
Yes it can be problem with the primer for one thing or an intake air leak.
 
One of the problems with the primer system is that the air cleaner base which the primer is in warps over time plus many techs overtighten them try to get them to prime. Once the base is warp or damage it takes reworking the gasket to make it seal. Often times here I use two gaskets shaving one in a way that applies pressure at the point that first gasket doesn't shows making contact during test fits. Once I get a good seal contact I glue the two gaskets together and tighten the screws to about 30-35 in-lbs. Or you simply replace the air base base and gasket; again paying attention as to not overtighten.
 
As the possible intake air leak there an o-ring on the beside of the carburetor can leak, also intake itself can crack since it is plastic.
 
On top of this if the engine has a lot hours on it, it can even be a valve clearance problem. The valve on L heads (side valve) engine tends to close up clearances leading to starting problems as the compression release becomes overly active.

That would the governor linkage and you need to do a static governor adjust now. As you move the throttle to full with the engine not running watch the arm and see which way it moves. Then you loosen the clamp, rotate the small shaft in the same direction as the arm moved to take up the slack and re-tighten the clamp.

Ok I was trying to do the static adjust. I'm a little confused about the throttle. Since this is the Toro Personal Pace.
You pull back on the bar, turn the key, and it runs at one RPM. So unless I'm missing something simple stupid.
I'm stuck.