Nice find. I agree, 66 or 67 judging by the shifter and the seat. Obviously the serial number will tell the whole story.
By the way, that is a Fasback, not a Stingray. Wheels and tires should be the skinny S-5 type. Front wheel is definitely wrong (can't tell from pic if rear is correct or not) and yes, it should have a front brake.
Just looked on eBay. There is a front wheel listed for $10 with no bids yet. Just a heads up.