There was a bit of fiddling with cameras in this thread Makie: Linking cameras in multiple 3d plots - #6 by Thomberger. I hope it helps. Maybe try to act on lookat as well.
For 3D axes are you sure update_cam! takes a tuple ? It seems it can take another camera, or update_cam!(scene::Scene, eyeposition, lookat, up = Vec3f(0, 0, 1))