@mksj
I do not understand what you are trying to say: "not show continuity with an ohm meter because it uses two reverse diodes" ... If the diodes are back to back (reverse) and in series, then they can never conduct. If they never conduct there is no current through the LED. Without current the LED does not light up. The light is a function of the forward current through the LED. If you really mean to say the two diodes are wired in parallel, but in opposite directions then one will conduct on each 1/2 AC cycle. i.e. there is current for each 1/2 cycle.
We do not know what is being used to measure continuity. @Christianstark has not said. Many modern electronic multi-meters do not show conduction for some diodes in either direction. This is because they use such small currents/voltages for the test. I have a half dozen modern multi-meters and they all do the same thing. However, I also have an old fashioned multi-meter that I have had for ~50years. It will show the difference because it simply applies 1.5 volts in series with a resistor across the device and then the voltage is measured across the resistor to determine the current flowing in the device. In the case of an LED, where or not the old meter will measure the conduction of an LED depends very much on the LED forward voltage required. Some times they are 2, 2.5, 3 volts to light up (conduct much).
Sometimes older is better!
Dave
I do not understand what you are trying to say: "not show continuity with an ohm meter because it uses two reverse diodes" ... If the diodes are back to back (reverse) and in series, then they can never conduct. If they never conduct there is no current through the LED. Without current the LED does not light up. The light is a function of the forward current through the LED. If you really mean to say the two diodes are wired in parallel, but in opposite directions then one will conduct on each 1/2 AC cycle. i.e. there is current for each 1/2 cycle.
We do not know what is being used to measure continuity. @Christianstark has not said. Many modern electronic multi-meters do not show conduction for some diodes in either direction. This is because they use such small currents/voltages for the test. I have a half dozen modern multi-meters and they all do the same thing. However, I also have an old fashioned multi-meter that I have had for ~50years. It will show the difference because it simply applies 1.5 volts in series with a resistor across the device and then the voltage is measured across the resistor to determine the current flowing in the device. In the case of an LED, where or not the old meter will measure the conduction of an LED depends very much on the LED forward voltage required. Some times they are 2, 2.5, 3 volts to light up (conduct much).
Sometimes older is better!
Dave