What's wrong with the one you have? If a part is missing/broken, a local blacksmith or machinist might be able to make it, at a lower price, than buying a whole mechanism.
You may not readily find a replacement, especially in new condition off the store shelf. If you did find one, it would likely be more expensive than you wish. You likely have to find a used one.... which means, buying a used chair and salvaging the mechanism. You may likely find a damaged used chair at a garage sale, on your local Craigslist or the like.... or keep an eye out, for one, on Ebay or Etsy.
I have an old mechanism, as that, but it has lots of surface rust... possibly/probably could be cleaned up with lots of effort. If you were close by (Lafayette, LA), I'd give it to you. For ages, I'd thought to fix the chair, but I still haven't bothered with it. I no longer have a use for the chair or have the drive to, simply, fix (hobby effort) old furniture (for myself, anyway). It's been in storage for 20-30 years, probably. *In the past, I've collected old stuff, as this, with the intention of fixing it, but never get around to it.
*Side note: For a vintage chair, as that, that caned seat looks new. Did you re-cane the seat (pressed-in cane, no doubt!)? I do some caning, as well.