The first place I would try is to contact the principal planner for your county's transportation planning department. The principal can be an ideal source for counts especially for roads not on the state system.
Be careful in identifying what type of counts you are obtaining. For example, there can be as much as a 25% difference between average daily traffic counts (ADT) and annual average daily traffic counts (AADT).
There are also vendors like Tactician where you can buy a subscription to use a traffic count data base and mapping system. However, there is no guarrantee that a particular road will be in the data base.
In the absence of historical data, you can purchase a traffic study from an engineering firm. Typically, the study is conducted over a 3-day period and produces raw 24-hour counts. The counts are averaged into a daily count. However, this count would also need to be adjusted for axle correction and seasonal factors before it could be used for car wash analysis.