Hi.
Mine doesn`t need to stay on once started ( it is the modern equivalent of a tickler after all rather than a true choke and pretty crude with it!)
All of the generic ones i`ve seen have a two-position notched rod that will keep it in place, and they have all been the same piston diameter!
I`ll take a look at what i`ve got and get back to you if you wish.
Cheers.
I forgot to add this last time -
https://www.ebay.co.uk/itm/Carburetor-P ... 4902.l9144