Blue Grouse is totally correct: MWT's have never figured in the proof test. The Proof House RECOMMENDED a MWT of 20 thou until steel loads became common and has now increased it to closer to 30 thou.
Ed Good: there are relatively few damascus barrels out there that measure in excess of 0.025" MWT's. They may have started life with nice thick walls but old corrosive primers, rebrowning etc have reduced most to high 20's at best, many are in the low 20's.
Karl Graebner: when measuring MWT's, you slide the barrel up and down the gauge looking for the minimum reading, whether it is just in front of the choke or just in front of the chamber.
I exaggerate because it is very difficult with a traditional MWT gauge to measure up close to the muzzle and most MWT gauges are about 15" long so unless one suspects something scary, one stops at that point from the muzzle.
There is no particular place that one states the MWT for, it is any spot on the barrel. If it was in a 'bad' place then I would state that in describing the gun.
As a point of interest, most barrels made in the UK from the last 1/4 of C19th to present do not taper from muzzle to breach.
They are often described at 'Eiffel Tower' profile, ie. they taper to around the mid point then the MWT's get slightly greater toward the muzzle. I understand that gives better dynamics to the barrel, reducing overall weight but increasing the strength of the tube near its end to accommodate the choke and risk of impact damage.
This means that if the bores are properly parallel (often not the case with guns that have been 'creatively' bored [!]) the thinnest MWT's measurement will be in the mid section of the barrels. On post 1880 guns, I find this is usually the case.