Yes, the choke is held open by detents, dimples drilled in the rod, and a small spring-loaded ball that fits into them. The parts drawing calls out 2, one in each carb, but you can get by with just one set in the left carb. If you inspect the choke pull rod, you'll see it only has detents for the ball on the section that runs through the left carb .....
There is a small hole in the side of the casting for the choke rod to drop the spring and ball in .....
As mentioned, maybe yours is just all gummed up and stuck "open". It's more likely the ball got lost. There's a good chance the spring is still in there though. The ball is a common 1/8" size.
Yes, you may need to go into the carbs again. It's pretty common not to get them totally clean the first time around. Another shortcoming of that video you put up is the guy doesn't stress the importance of blowing cleaner and compressed air through all the little passageways to insure they're clear. This is particularly important when it comes to the idle circuit. The fuel/air mix travels from the pilot jet and enters the main bore through 4 tiny holes .....
You must insure these are clear.