How do you measure continuity on long wires?

Easy: make sure both ends of the cable are completely disconnected. Go to one end of the cable, twist 2 cores together for instance brown and blue. Now go to the other end of you cable and test the continuity between the brown and the blue cables. This will verify both of these cables are continuous.
Now untwist the cables, and twist another pair together, say brown and green/yellow. Test again between these cable and you're done.

If you are fault finding, you can use this to figure out which cable is broken.

Say you get no continuity between brown and blue.
Set the test up again, test brown to green/yellow and you get nothing again.
Set the test up again, test blue to green/yellow... assuming you get a continuous signal here you can assume you have a problem with your brown wire.