Let's look at the core TN deities, and see what a TN cleric of each might campaign for.

Boccob. A cleric of Boccob might be a scholar or archivist that delves into ancient ruins for insight into magical phenomena. He might be a pious Indiana Jones who believes not with quasi-religious conviction, but with actual religious conviction, that ancient artifacts belong in a museum. Or he might desire to put an end to the evil necromancer because he gives magic a bad name.

Obad-Hai. A cleric of Obad-Hai might adventure for the same reasons as a druid. Perhaps said evil necromancer blights the land with undead, an abomination to Creation. Or maybe he wants to gather support for a campaign to end logging in a pristine forest, and the best way to do that is to clear out the bandits from the non-pristine forest. Or he serves the more human-centric side of his god and tends a flock of farmers, who have been oppressed by a horrible dictator. Though he wouldn't necessarily do so for any other people, messing with those farmers is the same as messing with him is the same as messing with his god.

Fharlanghn. This is the easiest of the three. A cleric of Fharlanghn probably adventures to see new sights and learn new things. He might wish to end a plague of bandits attacking travelers, or seek to stop a war that had resulted in the border between two countries being closed. Or he might want to protect a group of itinerant adventurers because he sees them as his god's natural interests.

Also remember that you can have a True Neutral character that believes in things like truth and love and altruism and fluffy bunnies so long as he's willing to murder, lie, torture, and decapitate kittens to achieve them.