Mechanical edge finders have one distinct advantage over other types of position locators ( electronic, Haimer taster, touch probe, optical, dial indicator, etc.). Properly used, they compensate for runout and so are independent of any spindle runout. The edge finder will automatically center itself on the spindle axis.
I run the edge finder at a medium spindle speed. I initially approach an edge relatively rapidly to get a rough location. I then back off to recenter the edge finder and approach the edge at around .0002"/second. I will repeat the measurement several times until I get a consistent reading to .0001". If you approach too quickly you can kick the trip out prematurely or you can shoot past as it's hitting the edge giving an inaccurate reading but my experience is that it is very repeatable.
For finding the center of a circular boss or hole, I will set the edge finder approximately at the the center of the boss/hole and find one edge in the Y direction and note the position. When using a DRO, I usually zero the DRO at that point. I then move to the opposite edge and locate it. The center of the boss is then 1/2 the distance of that reading. My DRO's re capable of making the calculation so I don't have to do the math. I then move to the center in the X direction and repeat the process to find the edges in the Y direction. If I want to be super accurate, I will repeat the X axis using the Y axis center although I usually find no change from the first position. I now have the true center coordinates of boss/hole. I do use care when moving the edge finder over a boss to return to the same z height for each measurement.
The mechanical edge finder takes longer than some other methods but IMO, it is the most accurate method of locating an edge. It works extremely well with a DRO but I used it for many years with just the crank dials. You do have to take into consideration any backlash in that case.