That is a matter of using the right tuners. There are plenty lightweight tuners on the market.I have built several 12-string bass guitars. And none of them suffer neck dive.I use Gotoh Res-o-lite bass tuners. And Gotoh Stealth tuners for the octaves.Because I kept getting comments from people who were sure my twelve strings bass builds would be one big neck dive fest, I did a little slap-stick in one of my demo videos:
This may be the most daring bass-related thing I've ever seen Gibson do. Not the best body style to do it on, but it does look cool. FWIW, my 8 string Ric with 8 full size tuners has zero neck dive, but I don't expect the same on a non-rev 'bird!
A Thunderbird then