I'm not sure the answer to this (I may have overlooked it in the rulebook) so any help is appreciated . . .

Does the keeper have to reveal the KEEPER'S objective? Meaning, when the objective card is revealed, does the keeper simply make known the player's objective only, and keeps secret the keeper's objective?

While playing through, "Return of the Reanimator" (1A), it seemed to make more sense to reveal ONLY the players objective to them, but not the keeper's objective.

To reveal both objectives seemed to be the equivalent of a movie or comic book villain standing up and saying, "This is my master plan! Mwahahahahahaha! Try to stop me!"

Yes.

"When the Objective card is revealed, it is placed faceup on the table in front of the keeper. From this point on, all players are free to read this card at any time."

(page 16)