Desire here is pictured as hunger, and the speaker can't switch it off. The refrain "the hunger never stops" returns again and again, and each time it is "hunting for you," as if the speaker were both the prey of an appetite and its hunter. The eyes wander over the other person's shoulders, back, neck and fingers, and the speaker longs most for the softness of a touch.
The feeling is more than physical, though. The speaker says it reaches past "the meaty and the tender" to something unnamed that "creeps and oozes." The speaker also seems aware that this devotion is unreasonable, calling it almost a crime and an ailment with no cure, yet keeps choosing it anyway.
The mood is obsessive, restless and a little dark, but also stubbornly loyal. The ending, "never will," feels like a vow. The speaker accepts the ache and doesn't expect it to ease.