In 1954 Hans Rademacher gave a series of lectures in which he described his reasoning step by step, see <A HREF="http://www.math.tifr.res.in/~publ/ln/tifr02.pdf">Lectures on Analytic Number Theory</A>, page 113 and following. This should give some insight into his creative process, of which he himself says: *"The path [of integration] is complicated and was
not invented in one sitting."*