mutter, grumble, murmur
呟 centers on low, indistinct vocal sounds: muttering, grumbling, or murmuring under one's breath.
呟 combines 口 (mouth) with 玄, which likely contributes the sound ゲン. The mouth component points to vocal sounds like muttering.
A mouth 口 beside the mysterious 玄: imagine someone muttering dark, mysterious words under their breath.
For ゲン, picture a grumpy genie muttering complaints from its lamp: genie -> ゲン, and the mouth 口 grumbles.