Re: What Types of Guitars have that Gibson 60s slim/tapered neck?
This is only going by what ones I've owned in the past: on Gibson's side, you have the '60 Les Paul Special DCs, the '76 RI Explorer, the SG Custom.
If you like Hamer, the 90's Special FM I had was pretty 60's slim taperish.
My Fender '62 AVRI Strat was squarely in the Gibson 60's slim taper territory.
I can attest to the above because I had liked the profile at one time and eventually sold them all to fund guitars with fatter necks.
I believe the following Gibson's also have 60's: Les Paul Classic, the Les Paul Standard now comes with a 60's neck as an option, Gibson's ES137, some of the ES-335s... heck, a lot of Gibson's these days don't have the baseball 50's necks that they were initially founded on. I'd argue that these days it's actually more difficult to find the thicker necks and 95% of Gibson's stuff is either some kind of fat 50's style neck or the 60's slim taper.
No. Most of the Customs have a neck profile that is specific to that model; neither '59 round or '60 Slim Taper. Some of the Historic Re-issues may have necks with profiles that correspond to their re-issue, but the run of the mill Custom has a unique profile. Guitar Center did have some '68 Custom Re-issues with the Slim-Taper neck.
Going from my 1960 Classics (ST) to the R8 (Ball-bat) to the G0s (custom, fatter ST), to the Supremes (LP Custom profile) to the Classic Antiques (SLIM Slim Taper!)--is a lesson in just how much each Gibson neck is hand-shaped.