Which of these four gene parts should allow the construction of the most accurate phylogenetic tree, assuming that this is the only part of the gene that has acted as a reliable molecular clock?]?

I believe the answer is Intron IV, Introns are non-coding regions while exons are the coding regions. In most eukaryotic genes, coding regions (exons) are interrupted by non coding regions (introns). During transcription, the entire gene is copied into a pre-mRNA splicing, introns are removed and exons joined to form a contiguous coding sequence.