How do I keep my cat out of a part of the house without a door?

The back of my house where my office and bedroom are get very hot during the day, but I cannot keep the doors open as my cat goes in there and chews wires. We have tried a 42" gate to the hallway of those rooms but he can jump it. He can't completely clear it, he jumps to the top, balances for a second and then jumps down. I read a tip online to duct tape plastic chopsticks upright on top of the gate so he would be afraid to jump on it, but I am not sure if that would work and he might hurt himself. Getting rid of the cat or covering all of my wires are not an option (way too many). Also adding another smaller baby gate on top is not an option as we go in and out of this area frequently and I am sure he would climb it. Is there a taller gate available with vertical bars or any other options?