This is a railroad term. If you fell asleep at the switch, you failed to switch the trains onto the right track and would cause a wreck when the trains collided with one another.

Asleep at the Switch - 1923 was released on:

USA: 14 October 1923

It means to fall asleep while sitting (or standing).

yes. it means you missed your chance

Dead to the world means sleeping soundly. One example of a sentence with the idiom dead to the word is: After working a double shift, Sarah fell asleep and was dead to the world.