I researched this when I searched for a replacement headliner for my Dearborn built 65 Fastback with an early September 64 build date. I can't recall my sources (Probably this forum!) but I found that early 65's had a white headliner (Yes, that would include October 64 cars.). I believe the time frame when colored headliners started being used was around December 64. As with many parts, this was a running change that was phased in when existing white headliners were used up so an exact cut over date does not apply. This makes sense with my Fastback. It's loaded with 64 1/2 parts like hood stops with the hole in the middle, one beveled headlight bucket (good example of early 60's quality control), Eaton power steering pump, wipers and bezel, vent knob with the "A" and carpet to name a few things.
UPDATE: I've found that many of the publications regarding this and many other topics have errors. The best advice I get is from the people on this forum. There are many well respected members that are more than willing to share their wealth of knowledge.