I recall listening to a documentary about it (just bits and pieces) — the second pilot watched Doolittle run off the end and drop out of sight, and by the timing he had to start his takeoff run after such and such a count. He’d started moving before Doolittle’s plane had made enough airspeed to rise where it could be seen from his windshield, but he started anyway, both trusting Doolittle’s calculations and not wanting to be shown up by him. :’) Also, the weather turned sour, which actually wound up helping them. They arrived at their targets from different directions, flying out of cloud cover. Japanese who happened to look up just assumed the planes were Japanese.
One pilot was so nervous he forgot to set his flaps for takeoff, but he somehow still made it.