It is a Singer 500a, Rocketeer. When I found it on craigslist. It was a frozen up mess.
Nothing would turn, the dials would not move but, the light would come on! I brought it home and did some serious oil and cleaning and now it is working pretty well. Ive got all the stitches working and the hand wheel adjusted. Now, I only need to get the feedogs cleaned out. The stitch plate lift is still frozen up. I hope to work on that today.
Here are some videos of me working the machine -