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Another tip- if you are giving him treats while he's out- he will almost always want to take them back into the cage. You might want to save treats for the end at first- though he will learn to come in and out to get them with time.
Depending on where you have the cage- you can always encourage him to venture out more on his own by making a connection. I've used long bird ladder, pieces of 1x4 wood, dryer vent tubes, etc- to connect their cage door to another surface you wouldn't mind them playing- like a dresser or shelf or bed, etc.
Also work on getting him to learn his name- and come when you call him. Rats can also learn to come to a clicker, a squeaker, a rattle, a bell- whatever sounds you choose to associate with them coming out and getting a reward for it.
Though a few rats can be ok on their own with lots and lots of human attention, the fact that your rat prefers to sleep than play does sound like he would do better with some more stimulation in the form of a cagemate. It is better to get him a friend while he is young- especially since you cannot predict your son's future interest or time- even if you feel the Rex gets plenty of attention at the present.
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