A Nikki Carburetor Fails Me Again

[MParr]

The last two times I went to cut my grass, my mower would not start.
This is a Gravely Pro Turn 260 with a Kohler PS ZT740-3046 engine. I checked spark. Good on both cylinders. I checked for fuel. The pump is working. One more test. I put my hand over the air filter horn. She fired right off. Hum? The choke isn't closing all the way.
I found the choke linkage laying on the bottom muffler shield.
Kohler part # 16 853 37-S

 

[Rivets]

Look at page 34 of this service manual. https://resources.kohler.com/power/kohler/enginesUS/pdf/16_690_01_EN.pdf

 

[MParr]

Look at page 34 of this service manual. https://resources.kohler.com/power/kohler/enginesUS/pdf/16_690_01_EN.pdf

I have the service manual.
See (F) page 36. There is a little gray plastic attachment part that is broken off. (F) was laying on top of the lower muffler shied with a piece of broken plastic attached to the shaft.
I believe a new carburetor will be needed.
Is there a cross to that particular carburetor?