I put a thread gauge on one and it is a #5-40 x 0.590" long. Length measured from bottom of head to end of threads. Overall length is 0.695".
It measures 3.09mm dia.
This is from a linear style flipper from my silverball mania. Not sure if the early flipper used the same switch so the length may vary if that is what you have. Either way, im sure the thread size will be the same.