testing signals on an ethernet cable

Ethernet is a "hertz" signal. You can not test it with a multimeter.

However, just because you are using an ethernet cable doesn't mean that ethernet signaling is being used. Simple signaling can be done over ethernet cabling, such as rs-485 or simple Form C signaling (such as used in relays, i.e. thermostats). Are you sure that it using ethernet signaling?

There's two types of ethernet cable testers:

1) Continuity testers, which only test that there is a straight-through electrical connection from one end of the cable to the other. These can be had for cheap, like $25 to $250 or so. all they test is conductivity and that the cable is wired properly. more expensive testers can detect more types of mis-wires.

2) Cable certifier, which in addition to doing most (if not all) of what a continuity test can do also certify that the cable meets certain specification, such as CAT5 or CAT6, etc.

If it's just form c signaling, you can use a multimeter.

You need different tools. The best you can hope for with a basic multimeter is basic continuity, which is better than nothing..but not by much. There are relatively cheap units that can confirm appropriate pin-outs, isolation, etc and there are higher dollar TDR-type units (Fluke makes some good stuff, but not cheap) that can actually certify the actual performance levels of the cable or - in the event of a fault - where along the cable the issue has occurred.