That Veritasium video has been completely debunked by people dedicated to studying and especially working with electricity. Derek is a hack and you should look for real science channels, not popsci slop.
I don't want to go screen videos right now, but his is vague and misleading about what it means for a bulb to "turn on". Putting current into a wire will also put a temporary tiny current spike into any adjacent wires. But that's it until the main current gets all the way around the loop.