watch intently
眈 centers on fixing one's gaze with deep, unwavering attention: watching intently, often with a focused or piercing stare.
眈 combines 目 (eye) with 冘, which likely contributes the sound and may suggest a downward or intense gaze. The exact historical development of 冘 is uncertain.
The eye radical 目 beside 冘 suggests an eye fixed downward or inward, as if staring with intense concentration. Picture a hawk's eye locked onto its target.
For タン, imagine a tan hawk perched on a branch, its eyes intently watching its prey: tan -> タン, and the hawk's stare matches the kanji's meaning.