I thought this was a really interesting post so dug out a few One-Trigger guns to play along. In each case, the trigger is functioning correctly. By that I mean the trigger fires only the selected barrel (doesn't double) and will not fire when on SAFE. All of course evaluated without breaking open the guns. Here's what I found (snap caps in every barrel - not to worry):

1. 1927 Trap Grade 12 Ejector (Selective Single Trigger) - I was ABLE to return the Safety to "Safe" after first firing either barrel.

2. 1929 Specialty 20 Ejector (SST) - I was NOT able to return the safety to "SAFE" regardless of which barrel I fired first.

3. 1935 Skeet Special Extractor 20 (Non-Selective Single Trigger) - I was NOT able to return the safety to "Safe" after firing the first barrel or second barrel.

4. 1940 Field 16 Ejector (Non-Selective ST) - I was NOT able to return the safety to "Safe" after firing the first barrel or second barrel.

5. 1950 Ideal 12 Ejector (SST) - I was NOT able to return the safety to "Safe" after firing the first barrel or second barrel.

Based on my samples, it would appear that they changed the One Trigger mechanism and/or safety between 1927 and 1929, but that does NOT square with David's findings. However, it does not appear that being a selective vs. non-selective trigger matters for this question. I think you probably will have to remove stocks to see the safety engagement with the triggers and if there are different variations. This seems like a question that Jerry Andrews could probably answer without having to disassemble anything.