Well, Singer made a lot of different machines, so if you could tell us which one you’ve got…
There is a possibility that it simply has no reverse at all. On home machines, reverse is often a tall button about 3/8" diameter that you push in, and it springs out.
I have an old Singer that took me forever to find reverse. It’s an about 15-year old embroidery machine, and the reverse is a touch-button right on the front, near the needle. Other odd places I’ve had reverse are a tiny hold-down button right on the back or side like gotpasswords mentioned, and also the inside paar of the manual reel sometimes pushes in along one side to start reverse.
I had a 99K from the 60s (it broke up with me, damn I miss that machine) and you controlled stitch length by twisting this lever till it lined up with the stitich length markers on the machine. In the lever-pointing-up position, it stitched forward at that stitch length. If you flipped it down, it stitched in reverse at the same stitch length.
If it is, then it is somewhat like Hello Again described: when you set the stitch length by tightening the knob on the lever on the right to the level you want, if you want to reverse sewing direction, just flick the lever upwards. I have a featherweight (all 11 pounds of it) from the early 1940s, and that’s how that one works.
Thanks for this tip! It was exactly the info I needed.
Just recently back to sewing on my Mum’s old Spartan and couldn’t find reverse for the life of me!