Recent work suggests that confluences, intersections between a symmetry-allowed branch and a same-symmetry branch of a seam of conical intersections are not rare occurrences. Therefore, with the goal of obtaining generalizable insights, confluences for the 1(2)A' - 2(2)A' seam of conical intersection in BH2, and for the 1(1)A - 2(1)A seam in HNCO are examined in detail using a perturbative representation of that region. The perturbative expressions for the energy and derivative couplings in the adiabatic representation provide a means for locating confluences and evince the significant effect a confluence has on the local topography and the derivative coupling. The perturbative representation enables the derivative coupling and energy to be determined from data for either. The results obtained from the more common energy-based description are compared with those obtained from a derivative-coupling-based description.