You could always put an alternate phone number on the billboard. You"ll still run into the problem of people looking you up in the phonebook after seeing the billboard, but you are guaranteed to be able to track some of the business back to your billboard.
I actually just worked on a similar problem (tracking internet advertising where 1/2 of all sales come from direct input of webpage address) with a local business owner, and I don"t think that there are any easy solutions.
One easy way to see if they saw the billboard is to simply ask, "Did you see our billboard on route xyz?", whenever a new customer calls. I think that will jog most people"s minds. If they are a first time customer, saw the billboard, and are calling you I think it"s a fair bet that you can tie at least a portion of their decision making process to that billboard.
You might also want to do a yearly customer survey to determine where customers are coming from. Additionally, I would add in something like a net promoter score as it is seen to have a high r^2 & low p-value in relation to business growth. After, you determine your NPS you can start figuring out both pain points with customers regarding your business, and the relative benefits or your business vs others. The real key here is to keep the survey relatively short so that individuals are willing to respond.
Amazon.com: The One Number You Need to Grow (HBR OnPoint Enhanced Edition): Frederick F. Reichheld: Books
pirate version of article
http://www.netzkobold.com/uploads/pd..._reichheld.pdf
Those are my thoughts, once you do that you can tie these metrics back go the billboard and determine whether it is cost effective or not. One thing not to underestimate as well is the value of brand building. The value of your billboard isn"t just that month but future months, so be sure to discount some future cash flows back to that month"s income.
Edit: I"m kind of rambling on here, but thinking about it if you are calling after the job is done to follow up on work performed that is a perfect time to determine your NPS, and see if there are any issues with the work performed. That way you are getting timely data (maybe you can track bad performance back to a specific team / manager / employee) and can act on it quickly. On top of this its a positive signal to clients that you care about the quality of work being performed. In a small business word of mouth is king. You might be doing all of these things currently, or might not have the resources to implement them, but it"s something to think about.
Elasticity of demand would also be interesting to look at for a service like yours. I"m not sure of a good way to go about this since you don"t have a standardized product, but imagine if you found that increasing your price increased your profit
andincreased your demand with affluent clients. It isn"t as far fetched as it sounds.