My oldest hit 40" at barely 3 years old. He wanted to do TOT at home when we showed it to him - but changed his mind once he saw it. The same thing happened at 3.5 years old. We just went back, and he's 6.5 years old now. My more adventurous second child is nearly 4 and barely 40". She went on TOT, which convinced him to give it a try as well. My daughter did great with the theming and pre-ride stuff, which I thought might scare her. But she did not like the flying off the seat part. So, she did it just once. (My other child did it twice). The ride didn't scar her though - she was willing to try everything she was tall enough during our trip.
I agree to show the child a video of it but also don't put any pressure on the child. I figure that as long as the child feels that he/she is in complete control of deciding, then it's fine to try. (Though I also put an exception on Space Mountain due to the seating. I wouldn't let a 4 year old do that but would let a mature 5 year old or any 6 year old do it).