If you have varying neck thickness, you don't know if your run-out is due to distorted necks or neck thickness. Misshapen brass causes the same problem.
Follow what Mikecr told you, he is correct. You need a ball mic to measure neck walls, and a concentricity guage for that purpose. No such thing as one tool fits all.
I have the Holland concentricity guage, and it works well, but I think the Sinclair may be a better tool.
If I were you, I'd stay away from thickness measurements with indicators though.
Something the article also missed is that you must have a means of setting depth from the case mouth, for the inner contact. Otherwise, on unturned brass, your measurements would not be at a consistent point around the neck.
With the Sinclair models you can drop washers over the anvil as a case mouth stop.
These things aren't cheap. But if you want straight brass, or tighter neck tolerances, it ain't gonna happen by chance. To find the best brass, it has to be measured with precision.