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you should first look at the pulley - every one that I have seen with a wobble was due to a bent pulley.
if the prior owner didn't know how to get the pulley off, it is easy to bend by prying it.
I'll second that, true on many Fords from this era. Hint: buy and use a proper pulley remover and then an installer (not the same tool). Voice of experience here...
No puller required on the sho to remove the pulley. If the pump is bad just replace it. It takes about an hour to change the pump with proper tools.