My dad served with this unit.They were indeed at Claiborne, LA.I have dates of when they shipped for England, went to France and returned to the US.
Departed for England 24 June 43 arrived 29 June 43 Departed for France 27 June 44 arrived 27 June 44 Depared for US 4 Aug 45 Arrived 12 Aug 45
He was a Platoon Leader Gen Serv Regt 1328 The organization is listed as: 392nd Engineer General Service Regiment.
He saved his 201 file with notice of unit commendations, dates of service, and generally what they did in England and France.
As a Platoon Leader G S Regiment he planned, organized, and supervised following const. work. Railroad building and repair, Railroad Bridges and Trestles, Camp construction as follows Barracks, Mess Hall, Latrines etc Sewage, Disposal, Roads in Camp
The one thing I did not find in his files was the name Dunham.