Hi Andrew,
Yes, that's what I'm doing for the within-subject variation. I'm interested if differences across individuals, accounting for their own intra-subject variation, are associated with a certain Independent variable. 

As an example, lets say we had a measure of cognitive performance measured across the 4 timepoints. We could look at how the within-subject variation in the task is related to within-subject variation of connectivity in the way you've suggested, by modeling the subject means.

However, I'm also interested in the connectivity of individuals who perform better overall compared to others. A simple way, I believe, would be to take the collapse the connectivity and performance across 4 timepoints, and treat those as 19 IV's and DV's. However, I'm wondering if there is a more elegant way which considers the intra-subject variability as well.

Thank you so much in advance for your help and time. Your help is instrumental in so many projects, mine included!