Do fully enlightened "persons" still meditate, and why? I get why they keep living, to help sentient beings. But does meditation help in that way?
Yes, Buddha did meditate. This is for the pleasant abiding here and now.
From the discussion, What did Buddha do to pass his time? --
Some relevant info:
Then the Blessed One, having emerged from seclusion after the passing of three months, addressed the monks: “Monks, if wanderers of other sects ask you, ‘By means of what dwelling, friends, did Gotama the contemplative mostly dwell during the rains residence?’: You, thus asked, should answer them in this way: ‘It was by means of the concentration of mindfulness of breathing that the Blessed One mostly dwelled.’ …
This means that right mindfulness functions not only as a factor of the path, but also as a pleasant pastime for those who have fully developed the path and tasted its ultimate fruit.
This quote is originally from the Icchānaṅgala Sutta (SN 54:11).