Yes, it is a Singer Red Eye. It looks like it has been well used. Two of my favorite 66's are those that were heavily used and the decals are thin-to-bare where the yards and yards of fabrics have rubbed its finish over the decades. Those machines are so smooth running.
There are several tut's in this forum on cleaning up and oiling these machines. Muv has a great video. If you choose to repair the veneer there is help for that in this forum also. Just do some searches here and on the www and you'll be able to get your new baby up and running by yourself.
Also, if you ask a questions here there will be many experts that will chime in with helpful advice for you.
You are right, there is a diamond in there
