Maybe I'm using the wrong term. Newer mowers like the one my neighbor bought(Honda) don't have a primer bulb like mine does. His broke down and the engine shop explained it to him like there was a wax cylinder that kept the engine choked until it warmed up and then the cylinder moved to open the choke once it was hot.
Yeah, that's an automatic choke (aka auto-choke) - the choke is adjusted automatically with no user involvement. As opposed to a manual choke that requires the user to adjust the choke to various settings when starting the engine, like on a chainsaw or string trimmer. Come to think of it, all my outdoor machines have a manual choke, including my chipper/shredder and snow blower. I could be wrong but I think manual chokes on consumer-grade mowers is a thing of the past.
My grandpap had a 20-30 year old Toro mower with a Tecumseh engine, which had a primer bulb (but auto-choke), I have a feeling that might be what you have. I sold it for $50 for the engine 12 or so years ago when he died - the transmission was shot and the cost was over $100 for the transmission. I don't think it was even OEM. So I said screw it, just sell it. The deck was built like a tank, but it was heavy as hell so using on a slope would have been not-so-fun.