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. ;-)