Think of runout as being similar to a car with a wobbly wheel. We've all seen that at one time or another. In the case of a rotor surface, any lateral wobbling past approx. 006" is more than the brake pad, pistons and piston seals can deal with and the result is the pads being pushed back from the rotor surface. The result is a low pedal that needs to be pumped to take up the gap and push the pads back against the rotor surface. An extreme case will push the pads back with such force that air will be sucked into the caliper around the edges of the lip seals. Frequent need to bleed the brakes is the result.
The cause of the rotor runout can be from any one of three or more sources
1) warped rotor (very rare on C2/C3 Corvettes)
2) replacement rotor installed and not machined as a set with the spindle
3) worn or improperly set up trailing arm bearings
It's possible to have more than one of these conditions at the same time. Measure and correct bearing end play first. With no grease and no seals in place, assemble the bearings and spacers using the set up tool instead of the real spindle and torque to required setting. The assembly should spin freely. Holding the trailing arm securely so that the shaft is vertical, place the indicator of the measuring instrument on any horizontal surface of the spindle (tool) assembly and set the dial to zero. Using hand pressure only move the tool along it's axis looking for free play. If this clearance is not within spec, increase or decrease the spacer size as required. Take lots of measurement in lots of places so that you're sure you've got repeatable consistent results.
Once final bearing assembly is done, but without the rotor in place measure the mating surface of the spindle (just for fun and practice). Most likely you will observe some indication variations, or wobble as you turn the spindle. Even if a rotor is dead flat, the is wobble will telegraph to the brake pad surface and lead to the problems illustrated above. Although it possible to move the rotor to one other position and still have the parking brake adjustment holes line up, most likely the runout will not go away. The GM factory dealt with this issue by riveting the rotor to the spindle flange and then machining them as a set. More common and what specialists like Gary R does is add shims between the rotor and spindle surface to cancel the runout. Gary goes one step further by bolting the new rotor in place.
To answer your runout measuring question, the tip of the tool should rest somewhere on the normal brake pad swept surface. The closer to the outer edge, the higher the readings will be and therefore be more accurate. Again, the more readings you take the better idea you will have as to what needs to be corrected.