Something is not right for sure about this so called "78" P bass.
I own an authentic 1979 P bass that I purchased brand new back in 1979. Way too many differences between my 79 and that "78".
As "ko Stradivarius" mentioned above, "no stamped "Fender" on the tuning machines and the wrong neckplate". My 79 neckplate has a single, large "F" on it, not "Fender, Corona, California"
When I purchased my 79, the bridge cover and pickup cover were included in the case but they were not mounted so my 79 doesn't have holes drilled in it for those pieces. And Fender wasn't mounting tug bars on those late 70's model P bass's. My headstock Fender logo and serial number are black letters highlighted in gold like the "78" though.
Maybe the person trying to sell this "78" bass replaced a lot of parts on it. But my 79's maple neck has aged gracefully and turned a more "golden blond" color due to it being 33 years old. And my bass hasn't been exposed to sunlight or nicotine to cause the neck to darken somewhat.
Personally, I would be suspicious of this bass unless the seller came clean with all the facts about the differences between an authentic 78 and the one they are trying to sell.
Here is my 1979 authentic Precision bass:
