Why do the nav lights on my micro stay on even after the battery is unplugged?

Those faint glows are almost certainly residual draw, but you need to figure out where that current is leaking from before you worry about killing the battery. It's not necessarily an ESC issue; the ESCs are supposed to cut power cleanly, and while they can sometimes hold a tiny charge, a consistent dim glow across multiple components usally points to something else. Often, it's a weak point in the circuit, like a hairline short in the LED wiring or maybe a bad contact point somewhere in the distribution block. If the planes were sitting for a while, the lights might just be drawing background current from tiny capacitors holding a charge, but if this is happening immediatly after landing and the power switch is off, you've got a persistent parasitic load. Even if it's just a couple of milliamps, that adds up over several days, especally if the plane sits in a warm environment.

To troubleshoot this, first try swapping out the lights themselves or the wiring harnesses leading to them. Sometimes the LED or its associated resistor fails in a way that keeps a minuscule current path open. If you can, test the circuit resistance with a multimeter after everythign is unplugged; if you see any resistance reading near zero (or very low), that's your leak.

If swapping components doesn't fix it, look closely at the main power switch and where the battery connects. Even small gaps or oxidized pins can create a high-resistance path that allows a trickle current to slip through when everything else is supposed to be dead. A clean, solid connection is critical for preventing this kind of drain. If it's a vintage micro, the wiring insulation might just be brittle and compromised.

Gotta disagree with the oxidized pins bit. A dirty or corroded connection makes resistance go UP, which means less current gets through, not more. Oxidation can't create a trickle out of nowhere, there has to be a live source feeding it. If the battery is truly disconnected and the glow hangs around more than a few seconds, I'd be looking at the switch itself or wether that receiver has some backup power path, not the connectors. Also swap the meter to amps mode in series with the battery lead and let it sit a minute. If it reads basicly nothing after the caps bleed down, you're fine leaving it hooked up over a weekend.

If the lights are dim and staying on, it might be the receiver itself, even if the main battery disconnect is clean. When I had a similar micro project, I tracked the bleed to the internal capacitor banks in the receiver board. Sometimes the filtering caps just hold a charge way longer than expected, especially if they're old. I once measured a steady 15 milliamp draw just from the receiver in a totally dead system. That's the difference between a quick drain and a slow killer. It's usually not the main switch or ESCs causing this when the draw is that low. You might need to physically swap the receiver for a brand new one just to isolate the component. That's usually faster than hunting for a microscopic bad trace on the wiring harness.

Total beginner take here but why not just unplug the little battery when you're done flying for the day? That's what I do with mine and it also keeps me from accidentally bumping the throttle while carrying it to the car. I got burned once that way, prop spun up in my hand. If the glow bothers you, watch how long it stays on after you pull the pack. Does it fade out after a minute or does it stay lit for hours? Might tell you if it's just leftover power sitting in the lights or something actually pulling from the radio box.

Might be worth checking whether the lights are even wired through the main switch at all. I had a scale-ish warbird years ago where the nav lights were hooked up ahead of the switch, so they'd stay lit till the pack was pulled. Drove me nuts till I traced the wires and found the previous owner's handywork. A couple minutes with a meter inline will tell you if current's actually flowing or if it's just caps bleeding off. If it's drawing real current, it's a wiring job, not a mystery.