Is the plug and harness at the back of the alternator in good shape? Might want to look at it closely, a good connection here is important. Unfortunately, the rebuilt units from the chain stores don't have a good track record on a 6.0 powered trucks. While they might work ok on a gasoline powered sedan, the load on them is pretty high with the diesel.
After going thru a couple of alternators myself, I took one to a local shop for repairs. After returning it the first time they fixed it by installing some different "heavy duty" parts and it's been working correctly for a couple of years now. Like yours the indication was an intermittent BAT light on the dash.