How can I tell where the other end of the conduit is?
Since you're talking about an electrical circuit with a line/load connection in each outlet, you can start disconnecting one side of the connection and then noting all the receptacles and fixtures that lose power, which will be on the load side of where you disconnected. You can go through a process of elimination. Typically, circuits are wired the shortest distance between outlets, so you can make some intelligent guesses at which junction to try disconnecting next. Of course only work on the wiring with the circuit powered off, use non-contact testers, and other appropriate safety procedures.

Another method you can try is sound. Pipe a small speaker into one end of the conduit, and then put a hose from your ear to the other end to see where the sound is loudest.

When trying to label cat5 that had been run around my home, I've shorted two wires together at each location, with a different colored pair at each place. Then from the other end I just checked for continuity between different pairs.