What kind of tape and how much did he eat? Have you seen any tape bits in his poo? Is he vomiting when he eats?
If possible move him to his travel/sleep cage or animal carrier. Keep him cozy and warm (not hot) and away from cold AC blasts. Provide lots of water in easy to reach bowls near where he is perching. If he isn't passing the tape and vomits when he eats, he is probably impacted (clogged digestive system) and the only help would be an emergency visit to the vet. If the tape is passing and he can hold down food, you might be successful with the very risky support-and-wait plan. If there is any way to drive to a vet, even if it's two hours away, that is probably going to be the highest chance for a good outcome since he is already showing serious symptoms.