I used to see 22 and 23 backs on eBay a lot. What seems less common is the 22, 23, RH12, RH8, and RH10/RH20 backs in 2x3 Graflok as opposed to 4x5 size.
Of course, the other issue is there may be frame spacing issues -- new film is apparently a little thinner than it was in 1950, and the Graflex 22 an 23, for certain, are turns-counters (as opposed to length counters like the RB67 backs). Mine works fine with Fomapan (haven't tried any other brands in it yet), but I have to be very careful lining up the start arrows on the film with the one in the insert. My first roll I overshot a little and got wide, increasing spacing with about half of frame 12 running off the end of the 120 roll.
If you want to check before risking film, you can cut a length of backing paper the same length as a 120 film and tape it into another backing paper, then wind that onto a spool as if new. Load and wind through, one frame at a time, marking the gate with a pencil at each frame. Once done, unroll the setup and check the marks. No overlaps, all on the cut length? You're good to go.