In this situation, there is no voltage when checked with the meter, so continuing with the meter will likely find the fault. You are correct to say that the meter will work
BUT
The reason why a meter isn't always the best tool to find a lack of power for something is simple.
Try this.
Put the negative lead of a voltmeter on to the neg of a battery.
Now put one hand on the positve of the battery, and the other hand on the positive of the meter.
What does the meter read?
Answer: Battery voltage.
You have 12 volts on your hand. Will it run anything electrical?
NO.
The resistance of your body will not allow any current if you try to put a current load across the circuit, Yet you clearly have voltage present on the meter.
If relying on meter readings, you may think the circuit is fine but it's not. An electrical device will not function here.
A meter will find an open( broken wire, etc), but NOT necessarily a high resistance(corrosion in a wire, thermal damage to a connection etc..), without adding a load to the circuit at the same time.
With a test light, the bulb is the load.
If it lights up, you have voltage AND a cicuit that will support a load
In the situation the original poster has put up, there is no voltage, so he will likely find the problem with a meter, if that is the way he goes with it.
BUT
A lot of the time, when "phantom" electrical problems are posted, about things not working, it's a simple error like this, that has caused most of the confusion, and made the diagnosis so difficult. You end up back at a circuit you thought was ok, but really wasn't