Reddit reviews EagleEmblems Eagle Emblems Men's 3rd Armored Division Tan Embroidered Ball Cap

This is the unit your great uncle was in:

https://en.wikipedia.org/wiki/3rd_Armored_Division_(United_States)

Just take a look at their WWII campaign:

Normandy
Northern France
Rhineland
Ardennes-Alsace
Central Europe

They were also called "Third Herd" or "Spearhead." According to the wiki they are inactive at this time.

EDIT:

Get you a khaki or black ball cap and have this bad boy sewn on the front, it would look cool: https://www.usamilitarymedals.com/products/3rd-armored-division-acu-patch

Never mind, THIS is better: https://www.amazon.com/EagleEmblems-Emblems-Armored-Division-Embroidered/dp/B07BS6N69Q

Pretty kick ass if you ask me.