That's a beautiful bass! I love seeing so many basses being brought back from the dead (ala Dr. Frankenstein or otherwise). I really want a shorty Fender for my boy's first bass. I need to do my homework and learn the differences between the Musicmaster and the Mustang...
I got my first Musicmaster (black '78) for my kid as a first bass, then I got into Musicmasters myself - I like their sound although I wish they were long scale and had wider string spacing - and bought him a '78 Oly white Musicmaster. Next was a '66 Mustang body and pickup with a '72 neck, and now this one from parts. Of the three, the Mustang is my least favorite.
The differences: post-76 Musicmaster necks (cloverleaf tuners, TV logo) are identical to Mustang necks. In fact my '77 neck has a Musicmaster headstock decal and a Mustang neck stamp. The Mustang has a split coil pickup (like a P bass but with smaller bobbins and one polepiece per string), the Musicmaster has a 6-pole single coil guitar pickup. Bridges: Mustangs are 4-saddle strings-thru-body (Musicmasters have top load 2-saddle bridges), and have individual felt mute pads on springs, like early J's. Body shape is also identical but Musicmasters have rounded-edges slab bodies, and later Mustangs have tummy cuts and forearm contours. Mustangs generally had nicer woods for the see-thru finishes. Also, some Mustangs had maple boards, Musicmasters never had them.
Here is a better view of the flaking finish, compared to a clean '78:
