Because of observing nesting patterns and interactions of mother and offspring (and because I don’t have a life and watch squirrels much to much), I have been able to track the variations in the head patch and dorsal stripes and confirm that specific patterns are inherited.  I am hoping, with a good zoom and knowing where they are keeping their babies, to be able to get close ups shots to corroborate my observations. I just thought you might be interested in data from a genetics standpoint. I know all my whites and who their mother is as soon as I see their faces.

Pookie and her son have a similar head patch and dorsal stripe, but his head patch is almost jet black and “sideburns” more distinct/ pronounced and his dorsal stripe is wider and darker and with less distinct demarcation lines around shoulders. But to the “trained eye” it is clear that they are related.
Incidentally, there No head patches in normal gray variants, There appears to be seasonal variation on head patches of whites ranging from “gray squirrel” coloring to pure black on same squirrel, particularly Snowflake, having watched over 5 years.