Warmest welcome to the forum Rmb2! We are certainly glad to have you here with us,I will try to help you out with a little information. According to Stanton's, the 125th Armored Engineer Battalion:
Activated: 15 NOV 1942 at Camp Chaffee Arkansas
Departed NYPE: 14 OCT 1944
Arrived ETO: 28 OCT 1944
August 1945 Location: Ampfling Germany
Deactivated: 19 SEPT 1945 at Camp Myles Standish MASS
Your grandfather's separation papers matches the ETO arrival date of 28 OCT 1944 for the 125th AEB, no guarantee, but most likely this was his unit. The 125th AEB was attached to the 14th Armored Division, which was also founded at Camp Chaffee. You do not mention what your grandfather's induction date into service was, it's possible that he was trained in the Thunderbird (45th) Division and then transferred to the 125th. Our gracious host Marion, may be able to shed more light on this, Good luck with your search.
Randy