Hi Nick,
Good question! Unfortunately, you are correct to suspect trouble. Imagine you are a Google bot. You go out to search the web for data about ABC Auto Pros and you find not one, but two, websites containing this identical business name, and also the identical address and phone number. You don't know which is the authoritative website (abcautosales.com or abcautorepairs.com), because the core NAP is identical. NAP may best actually be thought of as NAP+W (website) and this business' decision to have two websites means that they are creating confusion for Google. Also, because organic factors play so big a part in local rankings, this business is essentially splitting the authority they should have in half.
As I see it, there are three possible routes here.
1) The safest route: get the business to combine their two websites into one. Use appropriate 301 redirects so as to maintain as much authority as possible. This method fully remedies the situation and the business can then move forward with a totally clean and powerful approach. This is the approach I would most strongly recommend, despite the fact that it will involve a big change and lots of work. Fixing this now could save years of future headaches.
2) The patch-up: If the business wants to engage in Local Search Marketing and insists on maintaining two websites, only one should be optimized with the business NAP. The second website should contain no crawlable references to the businesses name, address or phone number - not in the masthead, footer, copy or tags. Essentially, this will make the second website something of a dead zone, but this is the only way I can think of to try to prevent Google from associating website #2 with the business. You would need to go through the website with a fine toothed-comb to remove any mention of any part of the NAP and also do a citation cleanup campaign to attempt to remove any references to that second website anywhere on the web. Even with this work , there is a chance that you won't be able to control all references to the complete or partial NAP out there on the web. Google just has to find one mention of ABC Auto Pros referencing website #2 to begin to become confused. So, while you could go this route, it's not sure to work and would involve constant vigilance of the SERPs to be sure that this association hasn't arisen.
3) The iffy idea: Note that I'm calling this iffy. There does exist a precedent in the Google Places Quality Guidelines for a business with multiple departments to be eligible for more than one Google+ Local Page. The language states:
Departments within businesses, universities, hospitals, and government buildings may be listed separately. These departments must be publicly distinct as entities or groups within their parent organization, and ideally will have separate phone numbers and/or customer entrances.
So, here, if the business had a separate phone number for the two departments and separate physical entrances for the sales department vs. the service department, they might be eligible for this approa_ch._ I say 'might' because this approach is most commonly associated with entities like hospitals and educational institutions. Google has long dealt with a history of heavy spamming in the auto sales vertical and, because of this, there is a chance that they would look with suspicion on this approach being taken by an auto-related business. I'm not sure. I would say that if the business does have separate public facing entrances for the two departments and can get a distinct phone number for the second department, then it would be worthwhile to go to the Google and Your Business Forum and ask the TCs there if they feel Google would be suspicious of an auto business taking advantage of this nuance in the guidelines. I would suggest you go by what they tell you there, because they see the problems and takedowns on a daily basis.
If you get an okay from them, then this would resolve your issue, as it would be okay for the business to maintain the two websites, optimize and promote both.
Long answer, whew! But this is one of those complex issues that requires careful thinking and good planning. Hope my thoughts are helpful!