Thanks, Bob. It took me a while to find it but Google says they're both correct.
Here's a question and reply from a site called "movie Mistakes."
Burt Lancaster is the 1st Sgt. of his Army company, the top enlisted man in the unit and in Army slang is referred to as "Top". The chevrons on his sleeve show the diamond insignia between three stripes on top but only two on the bottom. Top enlisted men in Army units such as 1st Sgts. and Sergeants Major have three stripes up and three stripes down. [Sorry but you are incorrect. At this point in time (pre December 7, 1941) the rank of 1st Sergeant WAS 3 up with 2 down with a diamond in the middle. It changed to 3 up, 3 down with a diamond in 1942. Also during WWII there WAS NO rank of Sergeant Major. Therefore Burt Lancaster is wearing the correct insignia.]
There's nothing there to indicate the date of the question or who to offer attribution to for the answer. (I am, however, relieved to note that after watching "Eternity" dozens of times over the years that I wasn't imagining a missing rocker.)