Hopefully this will be a quick and easy question, with a quick and easy answer, but why is it that we observe a perigee Moon coincident with a full Moon approximately every 13 months? Is this related to the Earth-Moon dynamics, perhaps the eccentricity of the lunar orbit?
The time between full moons is called the the synodic month, and the time between perigees is called the anomalistic month. The anomalistic month is shorter than the synodic month by about two days, (27.6 days and 29.5 days)
Since the anomalistic month is two days shorter, and there are nearly 28 days in a month, it takes about 14 months for the two cycles to come back into alignment. Thus there is a perigee at full moon every 14 (not 13) months.
More accurately the beat period between the two cycles is 411.78443 days. See wikipedia: https://en.wikipedia.org/wiki/Full_moon_cycle