I'm also a HUGE Paul Goddard fan.
Back in 1981, I was fortunate to purchase Paul's 1957 Fender Precision after he got an endorsement deal from Peavey. By then he also had his Ric 4001 and decided to let the old Fender go.
Paul sent me a letter on ARS stationery that outlined some the history of the bass. He used it on the first three ARS albums (Red Tape, Third Annual Pipe Dream and Dog days), plus recording work he used it on at Studio One in Doraville, GA with Roy Orbison, Joe South, The Classics IV and others, plus "countless live shows".
I paid $750 for it, and still have it. Here are pics of him onstage at The Fox Theater in Atlanta with the '57, and how it looks today. It still wears the last set of strings Paul put on it.
And yep, this is the bass that the "Another Man's Woman" solo was played on.