OICA production output statistics: OICA is the International Organization of Motor Vehicle Manufacturers. OICA provides sales and production statistics for all relevant countries in open data sets. These can be retrieved from http://www.oica.net/category/production-statistics/
EPA data: EPA is the United States Environmental Protection Agency. On their website one can find many openly available datasets: https://www.epa.gov/automotive-trends/download-automotive-trends-report#Full%20Report
Kaggle ebay data: Relevant data can also be obtained from Kaggle. I e.g. found a dataset on the German used car market. The dataset consisted of ebay postings from Germany and provided information on sales price, milage, year of registration etc. The dataset, which I have used for analyzing used car prices, is available here: https://www.kaggle.com/orgesleka/used-cars-database/data
data.gov fuel consumption data: Data related to automotive industry can also be retrieved from data.gov, e.g. here: https://catalog.data.gov/dataset/fleet-fuel-consumption and https://data.world/montgomery-county-of-maryland/5fa8def2-37b9-4abe-88. This particular dataset contained information on fuel consumption by fuel type, in Montgomery County (USA).
Time series data by US bureau or labor statistics: US bureau of labor statistics provides relevant datasets on their website. E.g. I analyzed hourly earnings in US automotive industry using data available here: https://www.bls.gov/iag/tgs/iagauto.htm#earnings
VDA time series data on German automotive industry: VDA is the German automotive lobby. The organization provides data on its website.
FRED domestic car production data: The US Federal Reserve provides public data on automotive industry too. There even is an interface available in R, in the form of the fredr package. You can read more about this R-package here: http://sboysel.github.io/fredr/articles/fredr.html