It's impossible to measure continuity with a voltmeter. Even if a digital voltmeter gives you some sort of reading, it will be worthless. You either need an ohmmeter or a DC milli-amp meter. Ohmmeters work on circuits WITHOUT a battery connected, and measure resistance. For the test you're attempting, an ohmmeter is almost worthless.
If you've got the usual type of digital multimeter, it will have a scale measured in milli-amps that can be connected in series with the battery cable to measure parasitic drain. Connect the test leads to the meter in the proper location to measure "amps" and disconnect one battery cable. Connect one meter lead to the battery post, and the other one to the cable. If there is any current flow at all, it should be less than 1/10 ampere, which translates to 100 milli-amps.
Jerry