So long as resistance is equal on all paths the electricity that takes a longer, more confused or circuitous route will arrive at the same instant as the one that took the shorter path. Distance is irrelevant to it, only resistance matters. The reason a bulb illuminates when you flip on a light switch is that you have just lowered the resistance on the circuit, from total (when the switch is off) to near zero (when the switch and lamp are on).
