(What follows goes outwith science.)
Pretty much all the geniuses I have heard of and who have expressed an opinion seem to say (in one way or another) that the key factor in their genius comes from outwith their conscious motivation - and feels as if it appeared 'ready-made' in their awareness.
In other words, geniuses will often decline credit for the essence of their achievement (and it is other people who often insist upon ascribing agency to the genius).
This means that - to a varying extent - genius seems to be experienced as a mediumistic phenomenon, that being a genius feels like being a channel for insights and understandings and inventions.
From these point, there may be a division among geniuses: crafted versus automatic. In other words, some 'receive' the inspirations, and work-out for themselves how to communicate it by craft; while other geniuses also receive inspiration about communication - for example, deliberately crafted writing from within the writer; versus a more 'automatic' kind of writing which the writer (to some extent) mentally stands-back and observes the emergence of communications.
The difference in these types crafted and automatic types of genius is seen when the product of a genius cannot satisfactorily be accounted-for by the observable personality and ability of that person.
Tolkien and JK Rowling could be taken as examples of the two types. Tolkien received his inspiration as 'given' him - as if discovered by him in fragments of ancient texts; and the achievement of Lord of the Rings can easily be understood in terms of Tolkien's own disposition, his abilities, what he wanted to do. When I see Tolkien in an interview is it obvious how a man like him would write LotR.
By contrast, JK Rowling's Harry Potter series (which is, in my evaluation, is also a work of genius - albeit lesser than LotR). But it is hard - I would say impossible - to understand Harry Potter as plausibly having been crafted by JK Rowling. When I see Rowling in an interview, there is a gross mis-match between the person and the work. I believe that the actual communication of Harry Potter was as a kind of 'automatic writing' - experienced more like taking dictation than crafting prose.
In support of this specific interpretation is that Tolkien felt a strong loyalty to LotR, and a gratitude for having the inspiration; while Rowling appears to be hostile to Harry Potter and has a detached, critical and revisionist attitude towards it - consistent with her not having had much to do with its production, but having mostly observed it emerging.
Where does personal choice and motivation come in?
The genius must accept the external inspiration; and the automatic type of genius must also accept the 'dictation' of the actual mode of communication.
Any attempt to interfere or reshape the external inspiration - or to select or distort the automatic writing - will result in a drying-up of the source of inspiration and loss of automatic writing ability.
However, inspiration can be refused, and distortion of communication can be attempted - with the above consequences. Genius doesn't happen anymore.
Presumably, this accounts for the frequent situation when someone produces a single work of (inspired) genius - but everything else they produce (which is entirely the product of the creator, and lacks external inspiration) is at a qualitatively lower level.
Most of these ideas are derived from A Geography of Consciousnesses by William Arkle (1974) 151-156.