As the Myers Briggs is not particularly valued among personality researchers (see here, for example), it is unlikely that you will find research explicitly focusing on this question.
However, the MBTI types Judging (and its counterpart Perceiving) have been shown to overlap with the Big Five personality dimension conscientiousness (Judging = more conscientious, Perceiving = less conscientious, see this earlier answer). Therefore, you can look for research on the relationship of conscientiousness and brain structures. A limited amount of research as explicitly investigated this question.
Quoting from a review by DeYoung (2010, p. 1173-1174):
Conscientiousness appears to reflect variation in the capacity for self-discipline and organization that is necessary for this form of top-down
control. Conscientiousness predicts academic and occupational success, as well as behavior that promote health and longevity (Ozer & Benet-Martinez, 2006). It is likely to be associated with functions of the prefrontal cortex, the brain region responsible for much of the human ability to plan and follow complex rules (Bunge & Zelazo, 2006; Miller & Cohen, 2001). A structural MRI study found that Conscientiousness was associated with
greater volume of the middle frontal gyrus in lateral prefrontal cortex (DeYoung et al., 2010), a region involved in maintaining goal-relevant information in working memory and in the execution of planned action based on abstract rules (Bunge & Zelazo, 2006).
There are some other studies on related constructs that may be interpreted as reflecting reflecting low conscientiousness (e.g., impulsivity, novelty seeking, and sensation seeking)
Again from DeYoung (2010, p. 1174):
Functional neuroimaging studies have found that individual differences in self-reported impulsivity are associated with neural activity in both dorsal and ventral regions of lateral prefrontal cortex (Asahi, Okamato, Akado, Yamawaki, & Yokota, 2004; Brown, Manuck, Flory, & Hariri, 2006).
Caution is required in interpreting studies of impulsivity, novelty seeking, and sensation seeking because these traits are heterogeneous in their associations with the Big Five, usually associated with Extraversion and sometimes with Neuroticism, as well as with Conscientiousness (Depue & Collins, 1999; Markon et al., 2005; Whiteside & Lynam, 2001). They seem to be compound traits, influenced by multiple more basic traits. Their
compound nature appears to reflect the fact that problems of impulse control may be exacerbated both by weakness of the top-down control systems that override impulses (the presumed substrate of Conscientiousness) or by potentiation of the impulses themselves, which may be responses to cues of reward (Extraversion) or punishment (Neuroticism).
Note that this is correlational research that can't answer your causal question.
For a critique of this line of research ("oversimplification") see here, for example.
Also note that the review I cited (DeYoung, 2010) is quite old considering how fast paced the neuroscience literature is. The review should get you started for digging deeper. I couldn't find a more recent review, but there are some additional studies.
For example, Forbes et al. (2014) compared people with brain lesions and found that
focal damage to the left [dorsolateral prefrontal cortex] (Brodmann’s area 9) was associated with high neuroticism and low conscientious factor and facet scores (anxiety and self-discipline, respectively). Compared with lesioned and normal controls, veterans with damage in left DLPFC also reported higher neuroticism and lower conscientiousness facet scores, slower reaction times on the California Computerized Assessment Package assessment, and lower scores on the Delis–Kaplan executive function battery. Findings suggest that while neuroticism and conscientiousness remain psychometrically independent personality dimensions, their component facets may rely on a common neurocognitive infrastructure and executive function resources in general.
References
DeYoung, C. G. (2010). Personality Neuroscience and the Biology of Traits: Personality Neuroscience. Social and Personality Psychology Compass, 4, 1165–1180. doi:10.1111/j.1751-9004.2010.00327.x
Forbes, C. E., Poore, J. C., Krueger, F., Barbey, A. K., Solomon, J., & Grafman, J. (2014). The role of executive function and the dorsolateral prefrontal cortex in the expression of neuroticism and conscientiousness. Social Neuroscience, 9, 139–151. doi:10.1080/17470919.2013.871333
