black, dark, unclear, private
黮 centers on deep, opaque darkness: something black, murky, or unclear. The sense of 'private' extends from the idea of being hidden in shadow or kept in the dark.
黮 combines 黑 (black) with 甚, which likely contributes a phonetic element. The character expresses deep darkness or obscurity.
The left side 黑 is blackness itself, and the right side 甚 looks like a container filled to excess. Imagine an overfilled pot of black ink, making everything dark, unclear, and hidden from view.
For タン, picture a dark tanning booth where the black light makes everything murky and private: tan -> タン, and the darkness hides you away.