I will add my 2 cents to this.
A $100 wallthickness gauge will do the job and is available at Brownells. You should modify it with a little spring clip to aid the reliability of the measurements as many here have done.
Most of the old gun barrels I've examined seem to have a double taper from the breach. The first taper is steep for about half the overall taper, then the second taper is shallower and goes down to the straight section of the barrel O.D.. From there on, the O.D. is constant diameter.
Barrels are manufactured by boring a larger diameter bar with a "gun drill" which is a single sided cutting tip to make it cut a long straight hole (believe it or not). The bore is then reamed and and honed to finish diameter. The bore is straight within a very close tolerance at this point. Then the O.D. is machined concentric to the I.D., sometimes over a mandrel. This results in a barrel that has the tapers and straight sections concentric to the bore within a few thousandths. When the barrels are soldered together and filed/polished is when the largest variation in wallthickness is most often introduced. Variation is furthered during any refinishing on older guns. You can often see it at the muzzles of a double where the outside wall is thinner than the area between the ribs.
I will add that a well raised dent that got honed and the outside polished should not have any thinner wall than the adjacent area. For the wall to be thinner, the outside would have to be "dished" by improper polishing. It does occur, but dent raising and refinishing doesn't have to result in this condition.
