The only way to try to narrow the date range of your specific instrument would be to remove the neck and check the butt end of the heel of the neck for a production date, which may be stamped or written there.
A Z0 prefix dates to 2000, a Z1 prefix dates to 2001 etcetera.
The neck date simply refers to the date that the individual component was produced.
Given the modular nature of Fender's production techniques, an individual neck may have been produced in a given year, placed in the manufacturing warehouse and remained in stock for a period of time, and then subsequently paired with a body to create a complete guitar in the following year.
In January of 1965, Fender was sold to the CBS Corporation.
The serial numbers do not immediately reflect the change, as CBS continued to make instruments using existing, tooling, parts, and serial number schemes.