I have the same model Onan. Went out to the driveway and removed the air filter so I could see the choke by using a mirror and flashlight. As expected for a cold engine, the choke was fully closed. In the picture below, the choke is on the left with the coil spring. I can move the rusty lever to the left to open the choke without moving the rod that goes to the other side an attaches to the bi-metal thermostatic spring.
Here's my best guess on how the choke is supposed to work. The choke is held closed by the coil spring until the engine starts. The high air flow with the engine running at speed then pulls the choke partly open to allow a better air/fuel mixture. As the engine warms, the bi-metal spring heats up and pulls the choke the rest of the way open, allowing a normal air/fuel mixture.
Without the choke rod to open the choke fully, you are going to have a very rich running engine. Perhaps it would be possible re-attach the rod to the bi-metallic spring.
