What does it mean when an LED bulb starts blinking randomly?
LED drivers are generally switching power supplies, which apply pulses of power to keep themselves charged to the level the LED needs. One side effect of this is that if there's a trickle of power available, they will still try to charge up, turn on the LED, immediately run out of power, and repeat. It's a complicated form of a "relaxation oscillator."

If your switch has a light or remote-control circuit that is powered by allowing a trickle of current through the load, or if you have a dimmer which fades far down but isn't cutting off completely, you'll get this effect.

For what it's worth, sample-to-sample variation means that different LED bulbs will blink at different rates for a given underpowering level. I have a 16-bulb fixture in my living room which, when faded down, does a nice imitation of christmas tree lights, "randomly" blinking in unpredictable patterns.