Having worked in the automotive industry my whole life and been through my share of assembly plants, I want to wager a statement:
As Rome was not built in one day, so weren't/aren't cars.
Many components and modules are pre-assembled off-line or even in a different plant (e.g: engine) and then "married" to the chassis/frame on the final assembly line. Early in the process of making the chassis, a VIN-number is assigned which follows the product through the build process. When the finished car finally rolls off the line and AFTER it passes final inspection, a build date may be assigned. Some vehicles may be routed to a rework area and have qc issues addressed. The final "finished" date is almost impossible to determine. Why it may be an interesting item to add to the history of your car, I don't see why it would be something of any value or even worth the effort chasing it. I am fine, knowing the month of production of any vehicle I own that has some remote historic significance. I do have that.
To add to the "food for thought" basket in this thread: I know of several car assembly plants that do NOT have any "Holidays". During full production, they run 7 days a week, 3 shifts/day with individual workers still working only 5 days, 40 hours/week. If demand slows, number of shifts are being cut, if it slows more, number of days/week is being reduced. Sometimes it is more expensive and a real effort to shut down and restart an assembly line, rather than keeping it running. It is hard to say what Daimler did in 1964 or 65 unless you could look at some company archives.
