I do not have the competence to indicate the part of the brain responsible for this I just wonder if reading widely and exposure to creative pieces would not address this age long problem that writers have been complaining.of.
I am curious in knowing which part of the brain that does that. But, what I know is that, sometimes, a writer may be in a fix or runs out of ideas in writing. We call it 'period of incubation'. During that challenging moments, s/he leaves the writing task and attends to other things. Later, the ideas in continuing the writing occurs to him/her like a miracle! (period of inspiration). S/he then returns to the work with joy and completes it. Writing is not a one time activity, it needs breaks and fixes in tightening all its lose nuts. This is part of the creative writing process.
no recent research has been carried out on this question. My own works on writing and emotions seems to target self efficacy as the main source of a writer‘s block: it often relies on stereotypes about writing (eg if you are in math you are not good with all things about writing!). Which of course is wrong!