Not sure I'm going to be able to help you here since I'm not sure if my clutch is original! But here's what I have...
In group 1.050 of the P&A, it shows the following:
1966-1967 Chevelle (396), 1967 Camaro (6 Cyl), 1968 Camaro (396) - Drive unit - P/N 986067 Unfortunatly, this is for the clutch and the fan assembly and doesn't have a breakdown of the P/N's by themselves. And of course, this could be a generic replacement assembly.
Both my Hollander and Mitchell interchanges (1969 editions) show the 1968 Camaro 396 as P/N 3927103. It also shows the 1967-1968 Camaro 302, the 1967-1968 Chevelle 396 (375), the 1966-1967 Full Size (427/425) and the 1968 Full Size (427) as using the same clutch. (Mitchell interchange #551 and Hollader interchange #175)
As you said, the AIM shows P/N 3916388, but it also shows P/N 3927103 as bing "Optional". There's also a note (note 4) stating that the 3927103 "WAS 3916589" with the change being noted on November 1st, 1967.
Now, to confuse things even more, here are 2 pictures of my old fan clutch. There's wording stamped into both sides of the clutch with "OD" stamped in black ink on the front side (see the pictures...) I have no idea if it's original so take this with a grain of salt!1968 Camaro 396/375 (L89) Fan Clutch front1968 Camaro 396/375 (L89) Fan Clutch rear
I hope this helped, but I know it didn't!!!