Depends what you mean by "slim tapper" because Gibson uses that terminology for almost any neck that's not a 59/58 baseball bat....
The LP 60 Gibson Custom Shop comes in two profiles:
- V2, kind of a C about 0.83" @1st, 0.96"@12th
- V3 thinner and with a flatter back than V2: 0.80"@1st and 0.90"@12th.
The V2 feels great to me, the V3 much less so but that's personal taste.
Many Epiphones have a slim taper; the last I tried was the LP Custom Pro and that one felt like an even flatter back than the Custom Shop V3 profile, pretty fast to play but not very comfortable for some chording style.
Despite equal thickness/width two necks, a neck with asymmetrical shape and more shoulders on the bass side will feel drastically thicker than a neck with symmetrical profile. Likewise a neck with V will feel thinner than C shape, etc..
I would say if V2 is what you have in mind then Pattern Regular would be the best bet, if V3 or thinner then most likely Pattern Thin.