Did TP sign his own guitar? Looks like it. The guy allegedly has one of the largest guitar collections around. Houses them in a warehouse in Van Nuys including some of George Harrison's guitars.
That photo is showing Petty with his own "signature model" Rickenbacker 660 12/TP, it's not necessarily his personal guitar he's holding in the photo.
Rickenbacker was proactive in signing up with guitarists who were prominently seen playing one of their guitars, and they'd contract with the artist to design a "signature model" which they'd sell and which had features specifically requested by that artist. This could be anything from the color, to the pickups, to more musician-specific features like Roger McGuinn having a compressor built into his signature Rick to give him that over-compressed "jangle" like Mr. Tambourine Man without having to chain together several studio compressors as he had done on the original record.
Tom Petty on his earliest albums and appearances was seen playing a solidbody Rickenbacker, one of the non-Beatles or non-Byrds models that was less common, so his 80's signature model reflected that.
The Bangles - one of the most misunderstood bands of the 1980's - were big fans of 60's garage, psych, pop, and British Invasion music. Their early concerts featured a lot of those covers before they became MTV stars. When they did hit MTV, Susanna Hoffs was seen playing a Rickenbacker more often than not. So they contracted with her for a signature model, and produced a beautiful guitar that's rare and not often seen. Terrific and beautiful artist, terrific and beautiful guitar.
Roger McGuinn: He and George Harrison (and Carl) put that sound on the map, so his model while not an exact copy of his Byrds-era 12-strings is what he requested for features, including a very unusual on-board compressor option which could help get the signature Byrds guitar jangle. The guitar itself is very similar to, but not an exact copy of what he used in the 60's.
Shortly before his death, they were working with Carl Wilson on his own signature model, which was *not* what eventually became the Carl tribute model, and not even what we know Carl to have played in the 60's, but rather a brand new model with features specifically requested by Carl for a "player's guitar". It never went beyond prototype, but those early designs still exist and are at Rickenbacker's factory.
I wrote extensively on the "real" Carl Wilson signature Rickenbacker prototypes here, with rarely seen photos:
http://smileysmile.net/board/index.php/topic,14847.0.html There are more examples, but here is a more complete rundown of Rickenbacker signature models:
1998 Pete Townshend. Three pickup 1997 w/ R tailpiece in FG. 250 produced.
370/12RM Roger McGuinn. Like a mid-60's 370/12, available in MG, FG, and JG. 1000 produced.
381 John Kay. 381 with HB-1 pickups and active preamp, available in JG (w/ black TRC). 250 produced.
350 Susanna Hoffs. "Deluxe" 350, w/ checkered binding and f/w inlays, available in JG. 250 produced.
4001 Chris Squire. Like a RM1999 with African Vermillion fretboard and headstock wings, available in Cream. 1000 produced.
325, 355, 355/12 John Lennon. "DB122" styling on all (355 model mostly had trapeze, 23 of them had the Accent). 2000 made between the three models.
230/2030 Glenn Frey. Like a 220 with silver trim, available in Jetglo (including fretboard). Run was supposed to be 1000, apparently far fewer were made.
360, 360/12 Carl Wilson. Like a mid 60's 360 or 360/12 with very thin tops. Available in Fireglo & Jetglo. 500 produced.
4004 Lemmy Kilmister. Like a "deluxe" 4004 Cheyenne, with checkered binding, star inlays, and oak leaf carvings. Three HB-1 pickups. Available in natural. Initial run of 50, later upped to 60.
Tom Petty 660/12TP: two toasters; trapeze tailpiece; 1 3/4" neck width (at the nut); checked binding; avaiable in Fireglo and Jetglo; 1,000 produced
Again, the photo reprinted is a little misleading as it's not Petty's guitar which he signed, but rather his signature model Rickenbacker. I may be mistaken, but I think I remember seeing that same photo in a print ad or in a promotional packet from Rickenbacker listing their signature models.