Use one in a Sporting Clays gun. It adds weight but not sure the mercury adds much to help manage the recoil. IMO, the additional weight is more helpful in balancing the gun to smooth the swing.
Here is some more info:
V. Mercury and Mechanical Recoil Reducers
These cylindrical devices are usually implanted in the butt stock of a shotgun, inserted into the empty chamber of a double, or screwed onto the end of the magazine tube of a repeater. Theoretically, they use mercury or a moveable mechanical weight that is supposed to attenuate felt recoil by spreading it out over a longer period of time. The claim is that the mercury (or mechanical weight) moves forward in the tube as the gun moves backward in recoil, thus "borrowing" some of the recoil energy and lowering the maximum amplitude of the kick. The weight returns to its start position, redepositing the borrowed energy, after the stock stops moving backward.
According to my shoulder, these devices seem to reduce recoil no more than adding weight in any other manner. (Adding weight, of course, does reduce recoil.) Dead Mules don't kick, perhaps, but they can nibble at your wallet. The mercury recoil reducers do add a humorous gurgling sound not available in stock factory shotguns. If mounted in the buttstock they also move the gun's point of balance back. This may be fine if the gun started out muzzle heavy, as many pumps and autos do, but is not so hot if the stock gun balanced properly.