be tired, sleepy
睏 centers on the state of being tired or sleepy, with the eye component 目 directly linking to drowsiness.
睏 combines 目 (eye) with 困, which likely contributes the sound コン and the idea of being trapped or weary. The exact historical development is uncertain, but the phono-semantic structure is plausible.
The eye 目 is trapped inside weariness 困: when your eyes feel enclosed and heavy, you are tired and sleepy.
For コン, imagine a con artist pretending to be sleepy, rubbing his eyes 目 while trapped 困 in a lie: con -> コン.