I am guessing by the VIN that your title may be wrong. The "S" prefix indicates the Shasta plant that was located in South Carolina. Roughly, this is what a '63 SCS would look like:
By 1978, the Shasta line looked very, very different, so if it something like this, it may well be a '63.
There are lotsa ways the VIN numbers got changed around during the history of many of these trailers. Most commonly was an assignment made for a lost set of paperwork, especially with a previous change of ownership.
Hope you'll stick around and share a bit of yours with us, we love the stories and the PICTURES PICTURES PICTURES!
As for your vin#, it shows that your Shasta was born in 1976 in Columbia, South Carolina.
A quick way to determine if your Shasta is an early 60's, it will have a rounded front & back, just like the picture posted by Ten. If it is a 76', it probably has plastic fender covers and will have a boxy front & back.
Pictures will really help to identify your Shasta.