Here are some comments on the early Browning Superposed twin single trigger. I do not profess to be an expert but I have looked at several and currently own 3. One of these is a receiver I bought for a supply of twin single trigger parts. I have disassembled them, and attempted to correct problems on a couple, one of which still stubbornly refuses to work.
When they are good they are very good. Trigger pulls are good, and it is sort of convenient to pull one trigger twice and still be able to select the barrel. However unless you do not use other double triggers, you almost never use the ability to pull the same trigger twice in a hunting situation. Instinct takes over, and you will switch to the other trigger.
The twin single trigger was not designed by John Browning and it shows. His designs tend to be characterized by rugged substantial machined parts that function unless something is pretty seriously wrong. (Think of the A5, the BAR, or a lot of other guns he designed) The twin single trigger is flimsy. Four critical parts are stamped, and the design works based on a proper balance between a light spring that holds trigger connectors in two planes, and the spring in the inertial block which must tension the block and also slide the trigger connections laterally. The thing is in some ways almost waiting to give problems. While interesting, it is very unlike a John Browning design. (If you disagree it is ok, as long as you have disassembled the triggers and corrected problems).
John Browning from his early years was fascinated by recoil and using it to operate guns. From the beginning I think he intended to have a recoil activated single trigger on the Superposed, but he died before the design was finished. I think the twin single trigger inertia system is at least in part an adaptation of his thinking. Val Browning finished the design of the later single selective trigger in the late 30s and the later design is very, very reliable and does not suffer from the weaknesses of the twin single trigger.
Originally the superposed had four different triggers: Double triggers, the twin single trigger, a single non selective trigger (which I have not disassembled) and a selective trigger with the selector beside the trigger in the slot where the second trigger would have gone. The double trigger was standard, the twin single a $20 option on an $80 shotgun. By 1936 the price of the lightning had dropped to about $70, and the twin single was standard. Shortly after that, the inertia trigger used on all post war guns sold by Browning was adapted and all other triggers were discontinued. My guess is that perhaps only 3-4000 twin single trigger guns were sold. By the 1960s (perhaps earlier) Browning would not supply parts for the twin single trigger and instead offered (for a fee) to convert the gun to the late inertia style single trigger.
I like the darned things, but I cannot say they are as useful in practice as they would seem to be in theory. Still, it would be very interesting if someone would manufacture one as an option, say on a Beretta over/under or perhaps a a Citori that was a replica of the pre war supers. I do not think the original Superposed design would be the place to start, however. A few other guns have used twin triggers that will fire either barrel sequentially but they did not seem to sell. Whether it was the gun, marketing, or just a solution to a problem that does not exist is open to speculation.