If the transformer has any markings as to manufacturer or model number it might be possible to find the application data on the web. There are web sites with vintage catalogs from Thordarson, Stancor, United, Chicago Transformer and others.
I had a mystery transformer with only a model number that I was able to trace back to Stancor by looking at the page indexes of catalogs HERE
Some of the old catalogs also include application notes, sample circuits and tips for selection and use of their products which could be useful even if you don't find the exact part. There is some consistency in color codes and pinouts within transformer types across manufacturers.