Fight / flight (sympathetic, quick), feed / breed (parasympathetic, slow). So the parasympathetic nervous system (PSNS) has three main areas, head (cranial) heart (kind of, vagus) and root (pelvic). I guess the bit you'd be interested in is the pudendal nerve in the pelvic, but this is actually sympathetic (quick) sort of relying on the parasympathetic (slow). See what I mean? The former gets the 'happy ending' but the latter is the thing that puts you into that position in the first place (Freud called it libido).
So how to support the PSNS? Exercise, good food, plenty of R&R (sleep, meditation, enjoyable downtime). Role of oestrogen? There are oestrogen receptors in both the sympathetic and parasympathetic systems, lack of oestrogen will, therefore, have an effect.
I work in Neuroscience research, not as an academic, and every single study always concludes exercise more, eat less processed food, get some decent rest. This appears to be true for a wide variety of people, e.g. Alzheimers, autistics, psychotics.