i was just thinking when you are testing for the ground wire, you might get one with a low ohm reading, and the other with a slightly higher ohm reading. the one with the higher ohm reading would most likely be caused by the reading going through the wire, through the coil of the relay to ground.
if i was you i would test it like this;
strip all three wires back slightly to expose some conductor
place them so they are not touching each other, or touching any ground reference
take your multimeter and set it to the VDC setting
turn your high beam on (in my ute i do not have to have the car on)
test each wire until you find battery voltage. turn the high beams off and the voltage should be 0. mark this wire supply, 12v+ or line
next test the remaining two wires to ground with the multimeter set to ohms and find which one has the lowest reading. might be something like .5ohms depending on run length and quality of ground reference. mark this cable as negative or ground as you please.
test the last wire with ohms again, hopefully it should read a higher ohm reading because it has the coil in the circuit to ground. mark this positive out, load, trigger or whatever helps you remember what it does. (i just just metered a 40a oex relay coil and it was 80.9ohms)
If it meters out like that mate you should just be able to put the 12v+ to one side of the switch and the load on the normally open side of the switch. if the new switch has no indicator light, just tape up the ground cable and tuck it away.
i'm only assuming its all 12v+ positive switch as well mate, other wise it'll be the other way around.
I'm not sure of your back ground or skill set mate, so I'm just trying to put it easy as possible just encase you've never dealt with this kind of thing before.
Best of luck and let us know how you get on!