When the battery is ruled out as suspect, you can use what's called "fall of potential" (fancy term for voltage drop) testing by connecting a voltmeter or tester's red probe to the battery positive terminal, and using the black probe to the point suspected of having too little voltage.UP, You may have good voltage, but do you have good grounds?
This also works to find poor connections on ground current pathways. Connect the meter's black probe to the battery negative terminal, and use the red probe to see how much voltage is being dropped between the battery and the point that should be at ground potential.
The voltage that is lost along the way will be indicated on the meter; obviously, less is better. A test light will also work, but bulb or LED brightness is not as sensitive. Ideally, there should never be enough voltage drop between any two points of the same circuit pathway to light a bulb.