It's usually the small spring that is wrapped around a small bit of the choke mechanism.If it comes off it's slot one side will work but the other won't.With the seat and the tank off you should be able to see where the choke cable comes through and the small thin wound spring I'm taking about is.

If I'm right you can hook it back on but may have to bend some of the wire/spring with a pair of pliers to make a better hook on it.
Also if you need your choke a lot then it may also be worth your while giving your starter motor a service.It's not hard,
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