Gretsch began date-coding serial numbers in August 1966.Date-coded serial numbers are typically found stamped on the back or top of the headstock, and "Made in USA" is stamped next to the number starting in June 1967. The next digit = last digit of the year (1966 to 1972: 6,7,8,9,0,1,2).
Most online guides (and quite a few print guides) are based on Jay Scott's groundbreaking book "Gretsch: the guitars of the Fred Gretsch Company," which is a fine book, but is nearly two decades old.
Subsequent research has unearthed quite a few inaccuracies in Scott's numbers, so any serial number guides cribbing from Scott are also incorrect.
Does anyone know anything about this sort of guitar, and why I can't find the serial number?
Gretsch used several different serial number schemes through the years.
In addition, these guitars followed no known numbering scheme.