Here is a suggestion I applied to myself maybe 10 or 15 years ago and is still applicable today but at a significantly higher cost fir some reason.
Go to Grizzly.com and look for a lathe with similar characteristics to yours. If it comes with a collet closer, you can buy the part you need by clicking on the list of "parts". You'll see an exploded view of the parts and a list with prices. If you don't find a lathe with a collet closer, look for a collet closer on its own, and buy the part.
When I did this fir my 12x36 "unmentionable", I paid either $25 or $30, can't remember exactly. I believe the prices today are on the order of $100 more. But it's available. I actually saw that part on eBay a week or 2 ago and told a friend to bid on it for himself. I think it went for about $90 or $100.
Good luck
Jacques
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