Ok I checked the choke and its working properly, opening and closing with the lever. It started right up no problem idled smooth at about 930rpm right after starting, after about a minute it had warmed up a little and was idling around 1080rpm. Seems fine at full throttle and driving around.
Heres some pictures of the what I think is the solenoid yall are talking about, the wires seem to be connected:
Pic one zoomed out for reference:
Pic two zoomed in under the Kohler Command Sticker to under the carb:
Pic three different angle: