Brilliantine is a sort of solidified hair product. Some of us who are old enough will remember our fathers using Brylcream which was a mens hair product with the consistency of cold cream. Todays equivalent would be hair gel. Apparently both men and women used the scented brilliantine, I imagine it would have made your hair look greasy but perhaps it just kept it in place with a bit of a shine.
This tin is in excellent condition.