I see more Red Eye models than any other. I have great Grandma's Redeye 66 treadle made in 1919 and the cabinet is with two drawers on each side, but missing the wide center drawer. It had been passed back and forth among my Granny, her sister, and my mother, so no wonder the drawer was lost. Years of sitting in the middle of our great Aunt's kitchen took it's toll on the veneer.
I had a conversation with the man who painted our house, telling him that each time I bought an old machine, I felt like I was rescuing it. He looked at me a while, smiled and said "I have a machine you can have." Later in the week I came home and he had left a Redeye in a cabinet, in good condition at my side door. It is in excellent shape. No name, no note, just the Singer and a more recent model of a Dressmaker that had bee partially dismantled. Each time I think of him, I smile.
Redeyes often show up on the Shopgoodwill.com site here in the USA.
By the way BKay, there is a horizontal cast iron brace across the back that would be under the machine and above the operators legs that has Singer cast into it, but nothing cast into the treadle like a name or model.