The serial numbers on the Singer site do contain some errors. Usually, though, it's a matter of the first or last digit of the s/n being filled in, obscured, rubbed almost invisible or made unclear. The letter O is confused for the numeral 0 and vice-versa.
Try looking at your s/n plaques with a hard raking light from the side - that will often disclose a missing digit at the beginning or end, or clarify that a C is actually a G or an O or something like that.
I don't think the Red Eye decals were put on anything but 66's.
Look at the pictures of the 127/128 in the manual and try to remember if yours has the sliding plates front and back that meet at a round plate under the presser foot. If yours has both of those plates and the round plate, you most likely have the right manual for that machine.
A round bobbin machine (15, 66, 99, 201) would have only one slide plate either to the left or to the front of the needle plate, which is usually D-shaped. Hope that helps!
