Here is a very convenient tool to figure out if your wiring is appropriately sized in your high draw pixel blade saber. I've book marked a typical application.Voltage Drop Calculator
Using Watt's law you can take these numbers and sort out the initial* power dissipation by your wiring.
For example, using 6" of 28awg wire, at 3.7v, with a 12 amp load we would see a drop of about .78V which is a 21.05% drop. Our guideline is that we should not exceed 3% and we should really aim for less than that.
P=IV, P = 7 x .78, P = 5.46 Watts
We can calculate the initial* resistance imparted by the wiring using Ohm's Law.
V=IR, 0.78v = 7a x R, R=0.111ohm
As you will see below, this will put your wire somewhere between "melting" and "catching fire." The wire is insulated so the heat doesn't dissipate, and as the temperature increases the resistance of the wire will go up. This creates a feedback effect wherein as the wire gets hotter the resistance goes up and it gets even hotter until an equilibrium is reached with the heat it's able to dissipate, or the jacket of your wire melts and/or catches a flame. This is why I noted these as the "initial*" values.
Strydur of The Custom Saber Shop performed experiments to demonstrate this effect:
I did a quick test using a power supply and a load generator. Keep in mind this is all tested with the wire we sell and could be different for the same thickness wire in a different brand. You would also get different results with longer or shorter wire, etc..
3" long 24 gauge
10A - Ok
15A - Hot
20A - Melt Casing
3" long 26 gauge
10A - Ok
15A - Melt casing
20A - Catch Fire
3" long 28 gauge
10A - Melt casing
15A - Catch Fire
source: Wire Gauge for Neo Pixel
In Tim's example of 3" 28AWG at 10A & 15A the power dissipation was: 10A x .32Vd = 3.2 Watts; 15A x .49Vd = 7.35watts
Keep in mind that if this was packed inside a saber, rather than a bench experiment, the effects would be worse. Longer wires will also impart an increased resistance.
In any case a melting jacket will lead to a great sadness, and possible injury.
There will be complicating factors like the contact resistance of your connector, the actual charge level of your battery, and the color of your blade, but with these examples and the mathematics I hope you have been convinced to appropriately size your hilt wiring for your pixel blade.