Capacitor to limit AC current, block DC current
This is something that an engineer just tries. Fortune favours the bold.

I always liked the 2 pin r/g leds - you get D1 and D2 in one led, and it is glowing both ways.

If you use modern hi-efficiency leds, in clear smt package (where you can see the die) then they visibly glow at crazy low currents. Obviously Red LEDs will be able to turn on with the least V.