I don't think you will be able to find this information because I don't think the data exists for the period you're exists. When we tie demographic data data to voting results (8 out of 10 Evangelicals voted for Mitt Romney, more than 9 out of 10 African-Americans voted for Barack out Obama), we're mainly basing this on public opinion surveys using a random sample of individuals. You can use complicated statistical methods to try to connect demographic data from the census to geographical data about polling precincts, but that's hard, especially for something like age, as most precincts probably have relatively similar age structures (and the ones that don't are by definition weird so we're not sure if they're representative of, say, young people in districts that aren't disproportionally young). And on top of that those ecological measures tend to have rather large margins of errors. So, in short, we need surveys.

Modern public opinion surveys really only start with George Gallup in 1935, predicting the results of the 1936 election. In theory, the 1936 election is the earliest possible date I imagine we could get turn-out demographics for anything more than total eligible or registered voters, and I'm don't actually imagine we'd get them before maybe the 1950's, and I looking through graphs on Google, I didn't see any with data from before 1960 (other than ones looking at eligible or registered voter turnout rates, which can obviously be calculated without public opinion surveys).