I think there is some incredulity of a 3-wire LED signal that requires AC voltage and does not work with DC voltage! But let's put aside the suspension-of-disbelief and re-state the application as simply driving a 3-wire 2-aspect incandescent signal from the Yellow-wire of an FT turnout. By incandescent signal, I mean something that requires a level of AC power that one would not expect the Yellow-wire to be able to directly light up. So now we're talking a relay...as fussing with a triac (an "AC" transistor) should not be one's first experience with DIY electronics. In my opinion of course.
There are many alternative but here's one I cobbled together with stuff in my parts stash. I do not have an FT switch to provide a proof-of-concept but I made some electrical measurements that convince me that it would work. The idea is to convert an inexpensive (less than $2 on eBay with free shipping from Asia) off-the-shelf 12V DC relay module to work with 12V AC.
But you have to surround the relay module with maybe 50 cents of "loose" components. The problem is you generally must buy 5, 10, 50, etc. of an inexpensive component which makes them no so inexpensive after all. I don't know the answer to the "minimum quantity" conundrum.
I did wire up the above circuit and it works over a wide AC voltage range - 10V to 18V - which I chose as what you might get from the Accessory AC transformer output up to O-gauge command-voltage.
As noted in my first diagram, this approach assumes that the black wire on the FT controller is the same as the AC-common (outer-rail). Again, I do not have an FT turnout but this can be confirmed fairly quickly with a meter.
For the technically curious, the trigger current into the 12V DC relay module was only 1.5 mA when driven by 5V DC. In fact, the relay module triggered with only 0.3 mA (with about 2.5V applied). So I'm fairly confident the FT turnout's yellow wire can supply this. Also, I confirmed this worked with a capacitor as small as only 100uF. This 12V DC relay module also operates down to about 9V DC.
Separately, while shown triggered by the FT turnout's yellow wire, this "design" can be used for the more generic insulated-rail trigger where wheel axles straddle the outer rails of 3-rail O gauge track. There are some minor changes but the cost is the about the same; if there is interest start a different thread so not to lose focus on the original problem.
