So, yes, apparently this was Timothy B. Schmit's bass. I didn't realize it at the time (the hang tag didn't say) but it's described on the website:
Fender Precision Bass 1959 | Gruhn Guitars
Didn't see any other pre-CBS P-basses at Gruhn or at Carter's (also went there), but both has some nice 70's Precisions and there was a Harmony at Carter's that I liked a lot. FYI the two Jazz basses you see next to the '59 in my photo are Custom Shop Relics, Gruhn had lots of Custom Shop basses including some really nice '51 reissues that were really well done.