Maybe my brain is overly-simplifying the question...
But a process for 'categorizing' ALL leads should capture this question. If your CRM supports assigning the Category, then the 'Process' starts with your Sales folks. Then at the end of the month any Up's that haven't been identified should be easy to find, as well as the offending Sales person who didn't follow process.
One of the additional wrinkles that could also be managed here, if your Sales folks comply, is you could track your Phone/Walk-in traffic that originated from your Website, or Cars.com or some other digital method.
That all said, this seems to be one of the very difficult challenges in-Dealership. For years the GM would love to know which Print, Radio or TV spot got the buyer off their seats, but even today, I am not sure there is a reliable tool to help with this. 
As I re-read my post for spelling, a thought came to me. A request to your CRM/ILM that Prompts/Warns the user if the "How Did you Hear" field is incomplete. You could further push those pop-up's into the Business Office, as they could also ask the question. I also bet that a Business Manager who is always getting pop-up's will engage the offending SalesRep to do his job...
Maybe some small spiff could be used for compliance. (Just thinking out-loud... I know you guys have thought these ideas years ago. )
