First, if he doesn't eat much, which may not sound serious in other birds, I would be concerned since I've never seen an Eclectus that didn't eat a LOT throughout the day. If you know that your bird was eating pellets before, even though my birds seem to do better on a diet of fresh foods, I certainly would make sure to offer him whatever he was eating before you got him. If you don't know what brand, size, flavor, etc.
Loss of appetite can be a major sign of illness.
Second, he might sit low on his perch. That posture indicates that he may be too weak to maintain erect posture. A healthy Eclectus looks very elegant with alert and upright posture, but sitting low, almost horizontally, on the perch is a sign of illness. Third, if he makes no noise to speak of and appears frightened all the time, it also could be a sign of illness. All of my Eclectus vocalize quite a bit daily, even if it is just bird sounds and not talking.