pupil of the eye
眸 centers on the pupil of the eye, the dark central opening that lets in light and reflects what is seen.
眸 combines 目 (eye) with 牟, which likely contributes the sound and may relate to the idea of a central opening or pupil.
The left side is an eye 目, and the right side 牟 looks like a cow 牛 with a mark 厶 on its head. Picture a cow's dark, glossy eye staring at you—that dark center is the pupil.
For ボウ, imagine a bow (as in bow and arrow) reflected in the pupil of an eye: bow -> ボウ, and the pupil is the dark target.