Well, guess we can't be too eager to jump the gun, for it could very well be authentic. It could very well be that the gentleman was a member of both units. There are many jackets and blouses around with unit insignia on both arms, this especially rang true of men who served in both WWII and Korea. They were entitled to wear patches from each unit they served with.

But, now we are all so eager to know all about independent engineer units and their attached assignments. I swear I learn something new almost every day. As I always declared, I will forever be an eternal student.

Warmly,

M1

Modern embroidered patches are made using a machine that requires a full edging process, and often have a little embroidered chain "tail" that hangs off the side.

The 10th Armored patch looks pretty new and like it has that wrap around, full edging process of a reproduction.

Good observation. I must confess I didn't pay attention to detail. Was too wrapped up in the ensuing conversation and research...

I am a little late to this conversation but figured I would add a few insights.  

When the men were being shipped back home, they did not always come back as a group.  Men with enough points would be sent home first and the fewer points you had, the longer you had to stay.  When they units were split up the individuals were moved to other outfits that were being readied to be shipped back to the states.  When that soldier came into the new outfit, they would need to wear that outfits insignia on their left shoulder.  As stated above, they were permitted to wear their previous outfits insignia on their right shoulder.  

So, for any given soldier, the outfit he came home in could have absolutely nothing to do with his service overseas.  One of my guys was in an engineer outfit that had been attached to the First Army, Third Army, and Seventh Army.  When he was sent home he ended up with the 26th Infantry Division (the Yankee Division) and wore their insignia on his left arm.  Even though he protested, he was still given and ordered to wear the Fourragère  the 26th had earned as a unit during the war.  They said that he was part of their division now and everyone must wear it.  

Also, if the soldier was in more than one outfit previously, he could choose which insignia he wore on his right arm.  For my friend mentioned above, the patch he wore on his right arm was that of the Seventh Army, the one he was with most recently (and probably the only one he had on him at the time).  For one of my family members, he chose the patch that he liked most from his past units.  That happened to be the Supreme Headquarters Allied Expeditionary Force (SHAEF) patch.  His reasoning was that he liked the looks of it and it was the one that Eisenhower wore.   

Thank you for your input. It's never too late to add to a post!