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So yep the wires were just in parallel so I could have just plugged it into the charger and left it "un cut" and let the Solar Charge Controller look after the voltages.
You can see that its just three cells in there... something I suspected but wanted to confirm.
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So the 12.6V rating is quite optimistic because it will only deliver that for a short time (as maximum safe charge on a Li-ION is normally 4.2V (unless you don't care about their lifespan).
Indeed it says 12.6 - 10.8V ... which is interesting as this means cells are pulled down to 3.6V (you know, 10.8 divided by three) and that's low for a lithium cell as normally you'd want to discharge them to around that at worst case.
None the less in my shed I expect that the lights will be on for no more than half an hour per day ... so all good.
So with the (quite compact) battery now prepped for sticking into my charger....
I did just that:
Of course I'll be measuring actual voltages as we get some time "in service", and not just relying on the controller's set voltages to be accurate (although I've found them pretty close).
But for $15 its pretty decent (well you know).
I'll let you know how it goes.