Leaking Bathtub Spout

I have an apartment with an old (looks old) Fairway single-handle shower faucet and spout. When the handle is in the off position and turned all the way to the right, there is a small stream of water leaking from the spout. Keeping it in the off position and moving it to the hot side creates an even heavier stream.
Do I need to replace this faucet? A gasket? A valve?
If so, any suggestions for removing the spout? It's somewhat rectangular and I can't find any screws..or anything.
Any information would be helpful.
Thank you, Patty

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