Some motion sensors, especially the lower end market type ( el-cheapos) are triac output and do not lend themselves to LED requirements.
Whereas other more expensive units use relay out so doesn't really matter a toss what connects to it as long as the LED has the correct drivers.
Plenty of places who will repack a battery for you if you are unable to do so.
Just be clear you want quality cells.
18550 is not as common a cell as 18650 so might be time to give up the habit or get a new unit.
You may have to speak to someone on how to upload photos acceptable to size regs but still visible detail.
As they are, repoduction is blurry there is not anything identifiable and way too small.
Whatever you do, short of blowing the innards, will do nothing to revive a lithium cell which has discharged below a set level.
The cells obviously have internal damage which will only be exaserbated by exposing to unregulated high current /voltages.
Voltage for a 3s pack at that level is beyond revival.
6.85/3 = 2.28V per cell......
About all you can do is take off the plastic wrapper and see which type of cell they are and go from there.
I suspect there are 3 x 18650 cells.
A couple of years behind you there Gears. so you would have been one of the 5 years apprenticeship mob.
Back when common sense was considered a fact and an attribute.:):)
Show photos especially clear close up of the suspect devices.
Also model/brand of inverter.
There may be a perfectly good reason why it is branded as 1000W.
I'd imagine 2.0mm would be standard.
What do you get as an average of the 12 pins..?
Remember that's only 11 spaces.
There are thousands of different types even without counting oem stuff.
One could start with Molex range.
AS an outside the box idea, one could get any 12 pin plug and socket...
You are aware the current transformer or whatever you decide to use only goes in one leg of the circuit...??
If, as you say, the cable size is for voltage drop, it would be quite acceptable to break gauge just for the measuring device, whichever, without any impact on performance.
Maybe for voltage drop at the low level.
Still, it's only 50 sq mm so probably no more than about 12mm od.(with insulation)
Don't know where the 20mm comes from.