Trick question, right?
A small gage wire would act like a fuse and possible open up before anything terrible happened. Or, the wire would dissipate enough heat to melt the insulation, and possible melt or catch on fire. A larger gage would hold up and something else would be the weak point. Wiring in an e-cig
mod is usually an inch or so. The resistance of 28 gage wire is about 5 milliohms per inch. 2 amps continuous through 28 gage inside a MOD would probably cause a temperature rise of 30 degrees C. In a very warm environment (inside a mod, up close to a hot running regulator) this might cause
cheap insulation to soften and melt. Better insulation would hold up. Anything less than 28 gauge and the temperature rise for the current carrying wires would be risky. 20 gauge wire is an over kill. The resistance is about a milliohm per inch. A couple of amps through this and you might see 2 degrees temperature rise.
28 gauge for the lead wire in a pass thru would be the smallest I would try. 3 foot length times 2 (both wires) is about 0.4 ohms, quite noticable. Voltage drop to a 2 amp load would be 0.8 volts. (Not a bad way to drop 5.0 to 4.2 though). Since the wire is usually in a open environment, not enclosed in a MOD, then temperature rise for good quality wire/insulation would probably be OK. 30% vaping duty cycle, 2 amp max load, would work. 20 gauge wire in a pass thru lead wire would never fail, it would survive a motherboard meltdown.
Got a feel for it now?
Rocket