Any idea on where to look up owner information on license plates of the past?

I'm happy that old license plates said in big bold letters the year & state, but I already knew that because my great-grandfather wrote on the photo. What I don't know is who the other people are in the photo that they traveled with. Was it a neighbor, friend, co-worker, or family member?

Any ideas how to find out who owned a car based on the plate number, year & state? This specific case is from Illinois in 1936.