I believe what you are seeing is leakage through a solid-state switch. The leakage is not enough to get/keep an incandescent bulb hot enough to glow, but can cause an LED to glow (or cause a faulty reading when using a high impedance meter).
It shouldn't be a problem for a daily driver, unless you have a lot of LEDs that are not controlled by relays. Might present a problem for a car in storage, but a trickle charger should do the trick.
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