The use of black powder and corrosive primers is a primary cause of pitting in some old shotgun barrels, especially if they were not cared for properly shortly after their use.  The results can be anything from slight to severe pitting and those pits effectively reduce the barrels thickness by the pits depth at that location.  If the shotgun bore is not mirror bright, a competent gunsmith will determine the depth of the pitting and take that into consideration when measuring barrel wall thickness for safety. 

With that said, here is a general 12 ga. guideline: 

In the forward 2/3 of the barrels length, a thickness of .025" has been suggested as a minimum thickness for safety reasons. The rear 1/3 length of the barrels, where the maximum pressures are exerted, requires thicker wall thickness.  The wall thickness at the juncture of the chambers and the forcing cone is the most critical and is where it has the highest pressure exerted. 

With some uncertainty, its assumed that a thickness of .090" at this juncture location would be about minimum. 

UK Working Standards recommended minimum wall thickness measured 18" from the barrel breech from Double Gun Classics p. 56, Vol. 1, No. 4 Jan-Feb, 2006:

2 1/2" 12g- .028
2 3/4" 12g- .032
Re-proof recommended minimum- .024

And, The Hunter's Encyclopedia from the German proof house: minimal wall thickness at end of chamber, regardless of length, for 12, 16 & 20 gauge guns should be 2.3mm (.0906") for 'ordinary good steel' or 2.1mm (.0827") if a 'Special Steel' was used. For the 24 & 28 gauges, due to their higher pressures, 2.4mm (.0945") was recommended.
Minimal wall of .6mm (.0236") was recommended in the "forward third" of the barrel.

There is greater pressure as the gauges go from 12 to 16 to 20 etc. therefore the minimum values might increase.

Learning the measurement of known original Parker barrels of the same gauge would be a good example to use to understand what Parker thought were safe values in the days when they were making shotgun.  The problem with this method is finding "original" Parker barrels and getting permission to take measurements.

The thickness of the barrel depends primarily on the frame size with respect to gauge, and secondarily on length. The barrels were finished by longitudinal hand filing to fit a general set of outside diameter checks. The filing was generally done to balance the gun at the hinge, but it could be muzzle heavy or light if the customer ordered. The longitudinal hand filing produced barrels that were not necessarily concentric with the bore, and wall thickness can vary side to side or top to bottom. There is no standard thickness.

Some guns appear to have thick barrels because full choke barrel muzzles are .040 or more thicker than the bore.

Again, without a hands on inspection, these numbers mean little; don't risk life and limb shooting bad barrels.  Have them inspected by a competent and knowledgeable gunsmith before shooting an older gun of unknown history or condition.

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