Simple switch with TLP222A
Continuity Tests should not be performed on a powered circuit. You will, most likely, get misleading results and, at worst, end up with a busted continuity meter. 

Also, you probably already realize this but the power and ground associated with pins 1 and 2, should be physically isolated from the power and ground associated with pins 3 and 4, or you're not getting much utility out of an optical-isolator.



Note you need a current limiting resistor, to limit the current in the path through pins 1 and 2 (which are the internal LED) to about 50mA, as per the test circuit in the datasheet (and the absolute maximum ratings table):



I'm pretty sure pins 3 and 4 are symmetric, but one of them should be connected to your load-side ground.