I think you do have a model 127. I've done research to compare the 27, 127, 28, and 128. The 28 and 128 have the 3/4 size bed and the 27 has the bobbin winder low on the column. It's just like a 27 so the manual for the 2 would be the same. Check the Singer web site for a manual.
It's a great machine. I learned to sew on a 27. Definitely clean it up and use it. There are several places online to get belts and bobbins. Just be sure the bobbins are the long ones. Some of the repros are shorter, I have heard, and don't work well. Do you have the shuttle? That is most important.