Ahh ok. That's a different story.
This is the relevant part of the electrical wiring diagram (EWD) for a 2014 LX
View attachment 3225354
First off.. toyota technically has two DRL systems on your rig. There is the LED strip, but also a step-down resistor (DRL MOD relay in the diagram) that provides less than full power to illuminate the High beam bulbs as the real DRL. At least on my 2013 Cruiser i can disable this in the nav system options, this may be the default on LX's, not sure. But all of that is in the diagram above.
You also can clearly see a red wire going to the three arrow sign.. on wiring diagrams that's the symbol for a light emitting diode. That's what you are looking for.
The thing that bothers me about this diagram is it is odd for toyota to have different wiring color schemes per side.. or swapped anyway. If you look closely the right headlight low beam is a black wire, and but that circuit is red on the left. Swap the colors for the high beam. Toyota does occasionally make mistakes on their EWDs.. and I did look at the 2013, it is different on these circuits. either way we can work around this since those aren't the wires you need.
Looks like the one you want is the DRL +12v red wire on each side. This should be on pin 5. if you look closely at your connector on the back where the rubber gasket is next to each pin well will be a very, very small number molded into the connector. This is the pin number. it should correspond to the numbers in the EWD attached to this post.
From your other thread, I see no pin numbers but a thick red wire and a thin one. It stands to reason the thick wire is for the high beam, but double check this with your meter. If that lines up, and as mentioned above should be a different color on the other side, check that pin number and figure out what's going on to find pin 5 and the wire you need.
Leaky's advice to use a relay is solid. Technically the wires you are looking for are already controlled by a relay, however without knowing how much current the DRL portion of the new fogs will draw, you are taking a risk. A properly set up relay system will eliminate this risk. You could easily run both new DRLs off one relay/trigger wire.