Simply by reading, one can develop a secondary field. For example, I could become a Balzac expert, and all it would take is reading Balzac as my primary reading interest for a few years. I could get through a lot of novels that way, and then read the secondary literature.
I recommend finding something that is not directly relevant to your field. Otherwise it is just an extension of what you should be doing anyway. It should be a different genre, language, or period from your normal tendency in reading. The time to do this should be taken from time otherwise spent binge-watching Netflix, or whatever else you do to kill time.
The purpose? You won't know in advance what the purpose is. You need to listen to a voice inside yourself that tells you what you need to be studying as your hobby-author. The purpose will be revealed much later, if at all. But the larger precept here is to be intellectually curious outside your normal zone of comfort. (It is the same idea as sleeping on the other side of the bed, as Clarissa suggested.)
The beauty of it is that all you need to do is read. If you are already reading, then you just have to redirect your reading in a particular direction, with a purpose in mind. You can get through all the plays of Racine in a year, easily, or whatever it is you want to master. Once you've read the primary texts and some secondary literature, you know about it. You can think about it and generate ideas.
I'm going to have to think about what author to read in depth. I think it's got to be one whom I don't know much about, in French because that is the language that I can work on most easily. It should not be a poet, and it shouldn't be from 20th century.