Since it's been professionally cleaned, we may assume it's not just half a century of grime (perhaps not). I've owned inertia operated single trigger comp O/Us for decades, and a well tuned inertia trigger is a joy to shoot. However, reduced loads may fail to cycle the internal selector, connector or whatever it's called in the gun in question. On the up side, there's usually an easy retrofit if you want to shoot light loads.
Every year, inertia trigger comp O/Us are tubed to shoot 4-gun Skeet. Somewhere along the line the reduced recoil of the smaller gun loads may fail to set the second trigger. Typically, it's a minor problem and easily remedied: the mass of the selector/connector's inertia block is increased. If they can made to shoot .410s reliably, light 12s should be no problem. Unfortunately, the Beretta trigger is more complex than some of the others.
I'm a Beretta O/U owner, but not an historian. Since the newer Silver Sniper will set the second trigger on light loads, the question is what, if anything is different? It may be a change in the inertia unit design or something as simple a lighter return spring. Also, after 50-years, there may be some corrosion impeding the inertia unit's travel. Perhaps a little polishing and light lubrication will put a new life into the old Beretta.