I live in eastern Europe, and I have a system where a double light switch controls two bulbs via a 3 wire ceiling fixture (my understanding is that two Live wires and a common Neutral wire). I want to replace my ceiling lamp, but there's a problem: the wires coming out from the ceiling aren't color coded, so I have 3 wires of the same color. How would I be able to find out which is which and how to connect my new lamp? Note that I have a voltage tester and a multimeter at my disposal. Thanks.
There should only be a single hot wire for a three way switch. The other two wires are known as "travelers" connecting the two switches. I would disconnect all of the wires and ohm them out one at a time from switch to fixture and fixture to fixture.
At the very least, disconnect power, disconnect the wires at the fixtures, and check for power. Once that is identified, the other two will be a quick swap if you guess wrong and nothing will get damaged.
Either way, once identified, you should be able to mark and reconnect them correctly.