Standard 2nd pitch we've always done goes out climbers left from the big tree up into the chimney/roof and then up to the same belay. Pretty sure that's the way Hill's guide writes is up.

Hill's guide does not indicate the chimney/roof combo for the second pitch of Second Coming - neither in words nor on the topo. Maybe you are thinking of Schein's guide "Sandia Rock"? Much better.

Anyway, I've never done the chimney variation so I didn't mark it on the photo.