With the hammer strut removed you have a SA only pistol. All other parts remain as designed and function as designed with exception of DA action for which the hammer strut is essential. Since it is removed, no more DA. DA hammer cocking and release is entirely different from SA release. DA hammer release is between the hammer strut and center section of the rear of the trigger bar. SA release is by rotation of the sear off the hammer hook. The pistol functions fine in SA but the first shot must be SA as well. So you have to cock the hammer prior to firing. The hammer strut has a small roll pin through the nose which pulls the trigger bar/trigger rearward when the pistol is in SA. This function will also be lost. No matter, install a pre-travel and overtravel stop. The trigger/trigger bar needs to actually move a very short distance in SA mode and reset distance is very short as well...perhaps 3/16" total trigger movement. All of this up to this point seems ideal for a target pistol with exception if rules require the pistol to have a DA action.
The pistol above has a JB Weld pre-travel stop and over-travel stop. What is shown is excessive, the trigger does not even have to move this far forward to reset as long as there is no hammer strut. It could have easily been moved 1/16" more rearward. Rearward travel depends on your hammer hook and sear work. Somewhere you have a matched pair; hammer hook modified and sear undercut for a 2 lb trigger. They must be installed together and not mixed with other hammer/sears. But the whole advantage here is minimum movement of the trigger bar. Fully resetting to DA mode requires a lot of trigger bar travel which makes all of this much more complicated clearance wise of internal fire control parts.
The two vertical legs on the rear of the trigger bar engage the two bottom legs of the sear. Rearward movement of the trigger/trigger bar rotates the sear off the hammer hook. When the ramps under the slide hit the trigger bar ears as the slide flys rearward the trigger bar is simply knocked downward and off of the sear allowing it to catch the cocked hammer. None of that changes with the hammer strut removed.
So assume we now have a cocked hammer and that the trigger is still fully rearward. What happens as we let the trigger/trigger bar forward. In a very short distance, 3/16" appx. the rear of the trigger bar clears the bottom legs of the sear, pop up in front of it and are in position to once again rotate the sear if the trigger is pulled. This will not happen if the hammer strut is installed, the trigger has to move much further forward for the DA/SA mode to reset.
What we need to figure out is how to fashion some type of lever that converts the forward moving trigger bar, after a shot has been fired, hammer cocked, sear engaged, trigger bar disconnected, into a rearward movement that quickly engages the sear, rotates it to release the hammer again which recycles the pistol but this time back into the conventional SA mode, trigger forward. This is the system you are asking about...binary trigger.
In order for this to function the forward moving trigger bar must have enough spring, it must engage some pivoting lever ( modified hammer strut nose), must pivot it quickly and cause the upper portion to release the sear, and not be in the way of hammer/sear movement as the pistol cycles again to the SA mode. Two shots fired, trigger now forward and ready for a conventional SA shot. Very little movement of the trigger bar seems essential to a simple design. Of course if you want a complex design retaining DA/SA capability an entirely different system will have to be designed. And that will be difficult in this small pistol. Somehow when all it said and done something needs to convert the forward motion of the released trigger into a rearward movement against the bottom of the sear to cause it to release the hammer a second time while the trigger is being let forward. 1917