Raggedman,
As far as I know, and I may be wrong, but the term “Squarehead” derived from the squarish helmets that were worn by German soldiers in the 1920's to the 1930's. This term was given to the Germans by the French. I am not entirely sure I have the dates correct, but I believe this is the era in which these helmets were worn.

I have done a little searching and have found a site with pictures and information on German helmets so if you are interested here is the link, http://www.1944militaria.com/original_german_wwii_headgear.htm

I hope this helps even a little,

Rev. Alimae

Rev. Alimae