Afraid of rabies, previously vaccinated. Walking outside on bright, sunny day (no rain). Single drop of liquid fell from tree and lands directly in eye/tear-duct. Couldn't identify source of liquid. Possible bat saliva exposure or being paranoid?

Paranoid. The most likely liquid falling from a tree would be water. Did it rain recently? The odds of a bat salivating in a tree on a sunny day is very very rare. Bats like dark places to rest during the day. Also, bats drooling? Also very rare. The saliva from a bat causing rabies comes from a bite, not drool. Also very rare to get rabies through the membranes of the eyes. So, please don't worry.
Not likely. Rinse you eye with clean water, if you have no symptoms of discomfort you are probably safe, if you do check with you medical dr or urgent care center. Rabies would be a real long shot.