The switch I'm using has three positions, and turns out this is critical to the success of this project.

Here's why:
I - using the original built-in battery pack. 
0 - no power source (this one turned out to be the critical part to the project, since it is required to power on the device while no power source is connected in order to discharge the capacitors. Turns out it will not power on if I just switch from one power source to another. The light would only blink shortly. However when I press the power button while no power source is connected (0 position on the switch) the battery indicator blinks shortly(discharging what's left in the capacitors), and then the device would work as expected after switching to another power source. 
II - using the external power source

Now that that I've put my idea to work, it turns out there is a little surprise:

The light will not power up if fed with 12.6V from my mobile power source(a toolbox that contains 2 x 3S7P battery packs connected in series plus a DC-to-DC step down converter (20A) which gives me usable 12.6v output.

However if I connect I directly to one of the 3S7P battery pack it would work as expected, since that's the same type of battery configuration that it has built-in. 

The battery packs I've created using li-ion cells from broken down ebike/scooter batteries and the green box 3S7P BMS kits that come from Temu. 

So my project is somehow complete, but I would like to push it to the next level, and use the connectors I've built in my mobile power source, rather than having to pull out one of the batteries from inside. This is inconvenient since it puts my batteries out of balance if I decide to use one of them. Or takes an extra hassle to take out both of the batteries and connect them in parallel to feed the light directly from the 3S7P packs.

I experimented by adding two 1N4001 diodes (connected in parallel) to the external power cable in order to induce a voltage drop. I did this order to test and validate my logic - 12.5 - 12.6v is too much to the device's liking. And yes - it did work, the device powered on successfully, however this did not last long since the diodes would heat up too quickly and even emit some smoke. At this point I've disconnected the device from the external power source and came here to ask for some help. 

So any community help is appreciated.
I am still learning the basics of electronics, and can define myself as being a novice/beginner.

And here comes my question: what would be the correct way to induce a voltage drop of approx 1v, without wasting the much needed energy from my mobile power source?

Thanks for your interest in my project, and thanks in advance to those who believe they can help me finish it!