Using a multimeter to see if ground is connected
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. DIY optical voltage probe.


Find an LED and a resistor around 1k (1000 ohms, brown-black-red) and make a probe. 
Connect the resistor to your battery and the probe to the location to be tested.
If the switching circuit turns on and conducts to ground the LED will light. Even a very short pulse will be visible.








simulate this circuit

Figure 2 (a) Negative-rail switching using a switch. (b) Negative rail switching using a transistor.

What you are describing is negative-rail switching circuit. i.e., the switch is in the negative connection of the load rather than the positive. Old-fashioned car interior lights used to be switched this way by a door switch which shorted the wire to earth. In your case the relay is probably switched by a transistor as shown in Figure 2b.