I use a tubing micrometer (aka, ball end micrometer) for this. I find it easier to get reading consistency with the micrometer held in a micrometer stand than held freehand, but these are cheap (Harbor Freight used to have one
like this for $10 at one point, though I don't see it there currently). They don't sell tubing micrometers at HF, though. At least, not that I've seen so far. That means that if you really want to go digital,
you will be out some money for such a tool. A vernier scale unit may be had
for a sixth the cost.
I usually find the amount of brass in necks is similar and therefore if they are thinner than average on one side they are thicker than average on the opposite side. This can be seen on a runout gage, as the indicator hand goes up and down fairly uniformly.