- For the Outline Toon "Shader" thickness: well, it's not actually a real shader that's creating the outline, it's a Solidify Modifier getting a special material assigned. And here's the problem: as the solidification goes too far out, overlapping geometry and sharp corners etc. can cause problems.
- For the missing outline on the neckhead: since it's the mesh getting a thickness through solidifying, this thickness depends on the faces' normal orientation. Maybe the faces of the neckhead are flipped? You can check that by enabling Face Orientation in the Overlays. If they show in blue, they are correct, if they are red they are flipped. You can also see it in the "spikes" when you turn up the thickness: the inward pointing thickness gets so thick it comes out on the opposite side.
