The edge finder has been my weapon of choice in finding an edge for more than thirty years. I usually make three approaches, the first rather quickly to get a rough idea of where the edge is and then advancing about .0001" every 1/2 second in the last 1 to 2 thousandths, repeating the procedure until I can locate an edge to .0001".
Approaching too rapidly will give a false position, either due to overshoot or if there is a small amount of wobble, kicking out prematurely. It has been my experience that once the edge finder kicks out, you have to back away by several thousandths before the edge finder settles back to a stable mode.
I routinely use my finger nail to recenter the edge finder after backing out about a thousandth as this reduces the amount of travel for the next approach. If I don't use my fingernail to recenter the edge finder, I have to back it out about 6 thousandths before it resets, at which point, there is a clear air gap between the edge finder and the work.