Well, the cases I've seen with the round type have a center pin. I'd have to go look again to make sure, but they cause the mechanism to move in and out, not back and forth. Yours looks like it needs something to move it back and forth.
From the other pictures you posted, your controller looks quite different than those for the round pin type. Though I wonder if mabye someone modified this to work with something they made - if they lost the Singer one. I'll have to go dig around because I thought I had the other controller type somewhere . . . Though since I know it didn't work, it may have gone in the trash.