Just to (hopefully) clearify things a little bit.
There are 4 parameters to consider when chosing a wire for an application.
1. Current (A)
2. Distance
3. Cross area of the leading metal, usually pure copper
4. Insulation type
1-3 are correlated in this way: the higher the current (A) and the longer the distance the wire should cover, the larger the area is required.
The smaller the area, the higher the resistance, =heat/Voltage drop=energy loss. (think lightbulb..)
The longer the wire, the higher the resistance =Voltage drop=energy loss.
4. Insulation type is determined by 3 main factors, Voltage (no concern of ours), surrounding temperatures and mechanical wear (vibrations yes?)
Actually high resistance/heat is something we absolutely don't want in our bikes, that causes voltage drop and dimmer lights.
That's why I will choose 1.5mm2 area wire which will take up to 10A without considerable losses.
1.5mm2 is actually quite a standard size in most households in Europe, but the stiffer type with one or a few strands.
Have built 2 electric cars and been doing some fiddeling with wires. ;-)