@rybergs I think you mean this…
… and as predicted it’s not Shrinkwrapped any more because it was drifting too much and intersecting the eyelids and eyeball, which wouldn’t be so much of a concern except that the intersections appear as black artifacts (even though the tear object uses a transparent material).
I’ve spent an inordinate amount of time trying various methods to get it as close to the eyeball/lids as possible without intersecting, and not so far away that there is a discernible gap between them - which is no mean feat, especially now that I’ve made the caruncle more mobile than it was before.
I was able to get the meniscus to conform more snugly by duplicating a ring around the eyelids so that it has the same weights and shape keys, and kept it as part of the main object. There are still some intersections happening in the caruncle though.
The difficulty of all this was compounded by symmetry going out of whack on a regular basis, as well as what I believe to be a bug related to this, which means I can’t use undo while making modifications to the basis.
Here’s what it looks like in motion. As you can see there’s still some driftage:
I think that was more info than you wanted though. 
@onnevan Not as yet, but I’m about to tackle the rest of the face rig so that will probably be back on the agenda shortly.