LED's can not be checked with a normal continuity test, they need to be checked using a diode test, and will have a forward bias voltage of approximately 2v. And yes they are polarity sensative.
Do not put a LED straight across 12v either without it having a current limiting resistor in series, otherwise it will go puff.
Some have an internal resistor, but vast majority do not
Will check manual later and get back to you if you can check it by pulling the wire of the top of the sensor and shorting it against it's body, the only diagram I have here does not show a resistor, and the sensor symbol is slightly odd, so I want to check the resistor is not in the sensor, it should be just a switch but ??