I have an American over/under rifle/smoothbore made by Ogden, Owego, NY. Two back action locks, neither of which has a half cock notch. Double set trigger.
If both hammers are cocked, pressing the trigger will fire the smoothbore barrel; continued pressure will fire the rifle.
If both hammers are cocked, and the trigger is set, the rifle fires first, and continued pressure fires the smoothbore.
If only the smoothbore is cocked, and the trigger is set, touching the trigger results only in a click. Continued pressure drops the smoothbore hammer.
The set trigger engages only the rifle lock.
Without a half cock notch, I assume the gun was carried capped, with hammers down. Don't bump a hammer!
I'm referring to the lower barrel as smoothbore. The gun is heavy, and has a crescent buttplate. It doesn't handle like a shotgun. I imagine it was a deer gun, the lower barrel being loaded with ball and/or buck.