According to Henshall, the etymological breakdown of 味 is pretty straightforward:
• 口 means “mouth.”
• 未, which has the yomi of ma(da), “yet,” means “unfinished.” In 味, the 未 component acts phonetically to express the ideas of both “good” and “lingering.”
So 味 refers to something good that lingers in the mouth. In other words, 味 represents an aftertaste.