Here's a setup to illustrate just how little current a modern voltmeter draws. The meters in the photo are hooked as in up in the drawing. All in series, you have:
1--HP analog VOM set to .25ma full scale. As you can see, it is barely off zero, inconsequential amount of current
2--Fluke 79 set to it's lowest current scale, 40ma. It is reading .001ma which may not be accurate. If it IS accurate, that is ONE microamp, a terribly tiny amount of current.
3--Fluke 77 still wired in series as per the diagram, reading full supply voltage, nominally 12V
In other words it is taking a TINY amount of current to operate that voltmeter, and I can assure you that 1 microamp is never EVER going to drain a battery, before it's internal chemistry does so
