The knee lever may be on the adjacent inside wall of the cabinet - so if you have not done so, look underneath and see if it's tucked up there.
The do slide right out - and if the cord is long enough to reach the floor, it's likely that is how it was used and someone just put it up there for storage. Most of them that were used with the knee lever have cords much shorter - and they won't reach the floor. It's easy enough to replace the wire if you want it longer - this style the pedal is the same.
There are a few different styles of pedals. I ave a Godzilla 66 where the pedal has a wing, and nothing mounted into the cabinet in the way of a knee lever. It's a later model foot control and looks more like newer types.
I personally don't care for the older Singer foot controls for machines I sew on regularly. I've replaced them all with more modern ones that have much finer control, and don't hurt my foot as much to use. The also don't get HOT like the older ones do. When sewing on ribbon, I've had to take breaks every 45 mn because the pedal is too hot to continue to use unless I put on a shoe, and I like to "feel" the foot pedal with the sole of my foot.
I had DH replace that one too - now I don't get a hot foot anymore!