Dating a Westclox Frank, Your Westclox sounds like one of the more recently made watches, ie 1980's. Westclox watches prior to around the late 1960's had the month and year of mfg clearly stamped on the movement (4 56 being April 1956. Toward the end of production some were stamped and some were not.
To check for a date stamp, you must remove the back. The back is a snap on type and is removed by slipping a knife blade into the crack between the back and case body and prying it loose. Look at the back plate for a date stamped onto it.