The rules for climbing onto a bigger creature are on page 271 of the DMG. They aren't extremely explicit, so there is a lot of DM input in how they work.
I just think it'd be awesome to build a character around this idea. Possibly a rogue/bard for that expertise in athletics/acrobatics.
I'd say, a safe bet is that in order to climb onto a creature you have to be two size categories smaller than it. So a halfling can climb onto an ogre, and a human onto a giant. That fits it neatly into the category, 'If you can't grab it, you can climb it.'
It gives you advantage on attack rolls and the larger creature's ability to attack their parkour annoyance is based on their location. Climb onto things backs and you could potentially be untargetable. They can still try and dislodge you but with a good base stat and expertise... you're fairly safe and it would take their whole action.
Pros:
-Advantage on attacks (not just weapon attacks, so if you feel like casting touchy spells...)
-Potentially unable to be attacked
-Move with the target, so you don't have to worry about those tiny legs or a fly speed
Cons:
-Takes an action as written(not one attack during an attack action)
-Doesn't work against medium or smaller according to my assumption (Maybe be an AT and take Enlarge/Reduce? Tiny Halfling! For some reason this reminds me of cheesy 80s horror movies...)
-Move with the target, so you could potentially get dropped out of the sky or dipped into lava etc.
So what do you folks think? Have you/would you use this mechanic? Do you think the 2 size category assumption is reasonable?