Generally speaking I don't google everything I read. But it's a good habit to get into.

This is what I read (overall)

• The headlights stay on for 10-15 seconds to provide a lit track or path for you.

Both my vehicles have that feature. Thanks @shortbus that explains a lot.

So the TS wants headlights to remain on for a period of time after shutting the vehicle off. As I said, mine have that feature built in. My wife's car - 2009 Toyota Venza - she hates it. So in the setup we set it up to NOT keep the lights on for about 30 seconds I think is about the time period my vehicles do the FMH thing. On my truck I've tried to disable that feature but have been unsuccessful.

My car doesn't have it sadly. The top variants did but anything under that doesn't.
P.s. What does TS mean

 

Been scrolling through the wiring diagram for your Toyota Motor Car (TMC). It's not so straight forward as one might expect. Perhaps a Chilton car manual might have clearer wiring diagrams. What I saw had multiple multiple multiple system specific diagrams. Knowing what you're looking for is the first hurtle. I looked for headlights and for multi-function switches. No, I didn't get through the entire thing, I got as far as the M's before I gave up. To someone unaccustomed to this sort of diagram it's got to be overwhelming. Maybe I'll scroll further down and see if there's a "Parking Light" section, but I think I saw something in the "Headlights" section.

Ping pong don't be discouraged. We'll figure a way to get you to where you're trying to go.

The parking lights are in the 'illumimation' section I'm guessing.
I'm more focused on the parking lights bit just turning on, not the headlights because the front led parking lights that I'm using are bright enough and wiring the headlights will just be a bit more complicated. Maybe I'll add those in the system but not any time soon.

 

So what I have in mind is this.
I am currently using the following LEDs up front:
https://a.aliexpress.com/_mqIfbHY
I have a time delay relay hooked up to them which is this:
https://a.aliexpress.com/_mtpTGlU
The white LEDs work as drls and as my current FMH setup. The relay is triggered by an ACC wire and the car central locking system. When It gets a signal from any of these sources, it turns on the LEDs. When the signal is lost, the relay counts down to 30s before turning them off.
So when I unlock/lock my car, the LEDs turn on for 30s. When I start the car, the ACC sends a constant trigger to the relay, keeping the LEDs turned on. When I turn off the car, the relay losses trigger signal and then starts counting down.
With this setup, only the front LEDs turn on, not the rear light/interior lights (basically the parking lights).

For this new project, I'll basically be hooking up the relay to the headlights switch.
What I understand is that the switch has a live wire coming in and then other wires going out to the fuse box. This includes the high beam wires, low beam, parking etc.
I'll splice the output wire from the switch that os for the parking lights and connect one end to the relay common. Then I'll add a jumper wire from the input live wire and connect that to the NC of the relay. This will allow the relay to send power from the live to the output from switch, basically removing the switch from the picture.
The trigger wires are going to be from the central locking system as it was before and then a wire from the switch that I spliced into. So the wire coming from the switch will be a trigger where as the other half that is going to the fuse box will be the common.
In this case when I turn on the switch, it triggers the relay and hence turn on parking lights as they normally would. Also when I unlock/lock the car, that too would turn on the lights for the set amount of time.
Another trigger will be from the light in the ignition switch as that illuminates as soon as I kill the engine for 15 seconds. So when I turn off the car, that too keeps the parking lights turned on for the set time.

I hope I was able to explain it all. Im not experienced in making diagrams but I could make a rough very rookie one to explain the switch input/output thing and how I'll connect it all to the relay.

 

What does TS mean

Thread Starter. We used to refer to the person who started a thread as OP, meaning "Original Poster" but some people misread OP as derogatory and therefore we no longer use OP. Once I used OP referring to the TS and he felt I was being derogatory and referring to him as the "Other Person". I had to explain to him the actual meaning. But someone here started using TS and it's hanging on.

Im not experienced in making diagrams but I could make a rough very rookie one to explain the switch input/output thing and how I'll connect it all to the relay.

As bad as you might be at it - it would still help. Schematics are a language all in itself, one most of us are well versed at. Even if we start with a crude drawing we can usually make heads and tails out of your drawing and maybe even give you in return a better drawing. Experience is one of many teachers. Mistakes also teach us what not to do. Don't be afraid to make mistakes. You won't be judged. Just guided.

 

As bad as you might be at it - it would still help. Schematics are a language all in itself, one most of us are well versed at. Even if we start with a crude drawing we can usually make heads and tails out of your drawing and maybe even give you in return a better drawing. Experience is one of many teachers. Mistakes also teach us what not to do. Don't be afraid to make mistakes. You won't be judged. Just guided.

Here is a rough sketch of the entire system. Again, I'm pretty newbie when it comes to making diagrams so please ignore any mistakes.

 

I have added a second relay down below which will break the circuit if the car is in ignition (Acc). I wouldn't want the parking lights to stay on while I drive in day for the set time on the smart relay.
But then there is a wire coming straight from the switch to the fuse box/NO of the second relay (the long stretch of green wire) so that if I turn on the parking lights from the switch myself, probably at night, it overrides the entire system and turns on the lights.
I'll add diodes in some places so that there is no reverse current. This generally includes all trigger wires, and the long stretch of green wire I was talking about above.

The wires are in no specific color, just added that in to make the diagram less confusing.