I bought a natural finish 1981 Flying V second-hand in 1990. Other than setting it up and restringing it regularly I've never done anything else to it until now.
The headstock looks genuine, is stamped 'SECOND', and a has serial number indicating a manufacturing date of 20 May 1981, at the Kalamazoo factory. The body cavity is stamped '(A)' and 'APR 23 1981', which fits the neck date, allowing for elapsed time between body manufacture and final assembly. The 'SECOND' stamp, used to indicate a cosmetic flaw, fits the manufacturing date ('SECOND', or '2' stamps were in use up to 1985).