I'm 44 and a thrill ride wimp but I can handle just about everything at Disney World - Mission:Space is a favorite, love Expedition Everest. Have a fear of heights but it things are over with quickly, I can handle it. Twilight Zone, however, still gets me everytime. It's not the drop, it's not the thirteen stories. It's the whole mind game they play with you before you board the elevator. After that, I relax. And I've seen the preshow dozens and dozens of times.
Some advice - you can see the drops from the outside so have your son determine if he'll be able to handle that. If he says he can, then go through the preshow stuff (the library and the boiler room). That's the mind game part (to me at least). If he shows any apprehension at all, when you get up to boarding the elevator, just tell the seater person that you want to leave. There's a regular elevator you can use to exit without doing the drop. Just about the entire elevator ride is in the dark. More mind games until the actual drop(s).
If he goes through with it, get him a pressed penny at the end to celebrate. The machines are right after you get out of the elevator.