There is currently running TV commercial for Howard Johnson's that features a background song?

The song is titled "~" by Andrew Bird and it is the twelfth track off of his Mysterious Production of Eggs album.

Depends which HoJo commercial you're talking about. If you mean the claymation one with "Happy" repeated, then that is the current cult mystery. No one knows for sure yet, even though it sounds like a song from our past.