As I understand it:
T1 is the power supply to both circuits
T2 is the ground to both circuits
S1 is the trigger for L1 which then splits and goes to each headlamp assembly (can assign it low beam)
S2 is the trigger for L2 which then splits and goes to each assembly and powers the high beams

So my question is can both S1 and S2 circuits run simultaneously if I put say a relay or diode from the high beam wire to the low beam wire? Or will it ruin the relay? Is this dual coil? I couldn't find a lot of info on the inner workings of this online.
Also is this SPDT, DPDT, or any of those others... I couldn't figure it out

 

This might be helpful.
https://moowiring.com/2023/05/01/dual-headlamp-relay-wiring-diagram/

Or this:

 

This might be helpful.
https://moowiring.com/2023/05/01/dual-headlamp-relay-wiring-diagram/

Or this:

I appreciate your effort but these do not answer the fundamental question of my post:
CAN S1 AND S2 BE RUN AT THE SAME TIME?

I have an aftermarket assembly with two bulbs instead of the single dual filament and would like low beam to stay on with high. Wattage of both bulbs combined will not exceed the rating of this wiring harness.

 

If you connect a diode between the high beam wire and the low beam wire, theoretically, as long as the voltage tolerance and rated current of the diode are appropriate, the S1 and S2 circuits can work simultaneously. As for the relay, things are a bit more complicated. Generally speaking, the coil of a standard relay usually can't withstand the current and voltage when the two circuits work at the same time. But if it's a specially designed relay, that's another story.

It's hard to tell whether it's a double-coil relay from the description. Do you have a more specific model number or circuit diagram?

 

If you connect a diode between the high beam wire and the low beam wire, theoretically, as long as the voltage tolerance and rated current of the diode are appropriate, the S1 and S2 circuits can work simultaneously. As for the relay, things are a bit more complicated. Generally speaking, the coil of a standard relay usually can't withstand the current and voltage when the two circuits work at the same time. But if it's a specially designed relay, that's another story.

It's hard to tell whether it's a double-coil relay from the description. Do you have a more specific model number or circuit diagram?

Sure. Lemme give as much detail as I can.
Website sales links:
https://www.philips.co.in/c-p/LUM12...r-max-brightness-on-the-road#see-all-benefits
https://www.philips.co.in/c-p/LUM12...relay-for-max-brightness-on-the-road/overview

There is no real technical data sheet on their website as best I could tell.

In car diagram:

There are a lot of videos explaining how to set one up on youtube. They also kind of explain how it works but don't define the inner workings or if S1 and S2 can run simultaneous. My assumption is that it's two 4 pole relays put together so that they share the ground and power wires but each relay is independent. But I have no evidence to base that on.