Junior, that demo was in a thread with an infrared-optically triggered occupancy detector (e.g., MTH ITAD or Lionel 153IR). The yellow-to-green time delay uses a 12V DC "delay on" relay module. What is/was not shown in the video is the need for a 12V DC power source. Additionally, optical triggering provides "free" electrical isolation between the DC voltages needed to run the timing electronics and the AC voltages on the track insulated rail trigger section. So all this techno-babble means it's a bit more complicated than 2 modules.
But in the DIY hobby spirit, I cobbled together the following. Short video first!
And here's what's under the hood. I don't know exactly what kind of signal bulbs/LEDs you have but I found I have a mock-up of a 4-wire common-anode LED signal with a 1000 Ohm common resistor. As I recall this is what you get from eBay seller "we_honest". Of course we_honest sells signal controller boards including one with timed-yellow.
What I came up with starts with the 2 modules I showed earlier to drive the 2-aspect red/green signal. So there's the AC-to-DC converter (far left) set to 12V and the 12V relay module (bottom). The 2 modules function pretty much the same as before. That is, when the insulated-rail section is triggered, the relay turns on and applies power to the RED LED.
The modification is when untriggered, rather than powering the GREEN LED, a "Delay-ON" relay module is powered. When you apply 12V to a Delay-ON module, it waits some settable time-delay then turns ON. So during the delay, the YELLOW LED is powered. After the delay, the GREEN LED is powered...and stays powered until the insulated rail is triggered again.
The 4th module is a second AC-to-DC converter. In this case I show one that has a fixed 12V DC output. It could have been a second adjustable converter (set to 12V) but I didn't have one handy for this demo.
So while there's still "no soldering required", the cost has jumped to 2 AC-to-DC converter @$2.39, a 12V relay @ 97 cents, and a 12V delay-ON relay @ $1.17 so about $7 (free shipping from Asia). But it does seem a bit complicated considering there are off-the-shelf solutions.
But, if you'd like to pursue this if for no other reason than to mess around with relays, learn more about LEDs or AC vs. DC interaction, or whatever then I will gladly draw up exact wiring instructions and/or discuss alternatives!