Sorry if I came across the wrong way but your suggestions just seem rudimentary. I've been working in the electrical field for 23 years, and though I admit not to understand the electronic side of things many, of the same principals apply.
The voltage at the input of the ballast must be 12VDC, how can it be anything different. Other then the contacts and the wire from the battery there is nothing else to create voltage drop so it must be what the battery is putting out. Are we not on the same page with this? That's the reason I find this troubleshooting recommendation odd, unless I'm missing something.
I mean no disrespect and appreciate your feedback and input. I've got some troubleshooting procedures in mind but they pertain mainly to trying to figure out why the DRL lighting switched.