I got a NOS Gemline replacement cold control for my '57 GE from Larry at Modern Parts (RIP/Pieces) and it was an easy install. The control came with a large assortment of brackets, other mounting components and adapters so it could be installed on various makes in addition to GE.
I'm pretty sure I tossed the Gemline box that had the old control in it after the fridge suffered a catastrophic compressor failure and was hauled away, but if I do come across it or the invoice for it, I'll post the part number here.