The extra timeline allows for Wayne to evolve in ways unique to True Detective, and he later falls victim to memory issues, among other overarching mental troubles.
With Wayne known for his unwavering attention to detail, it’s easy to understand why he becomes so haunted (figuratively and literally) when his faculties start fading.
As it’s hinted at above, Wayne bears much in common with Rustin Cohle, from his deliberate word choices to his underlying obsessions with unsolved cases, though the comparisons are surface-level.