Oftentimes, troops stayed in Beaumont for brief periods because the railroad passed through it. You can find a lot about troops in SE Texas by reading Moss Bluff Rebel. The only mention of Orange is about seeing it from the Sabine River.
I never heard of a garrison in Orange, but troops passed by on transport boats often in route from Sabine Pass to SW Louisiana. Spaight's Battalion traveled through SE Texas alot and are mentioned in the above book.