I was listening to this today on Join the Dots and was reminded how much I've always loved this song, but especially the line
The little time I spend with you we drink each other dry
Overall, I think the song is about finding or noticing someone you think would understand you because they are the same kind of strange.
That particular line, though, makes me think of instances in which you may only see someone rarely (like maybe you are in a class with them for just a couple of hours a week, or maybe you run into them for incredibly brief periods of time on a regular basis on your commute) but you anticipate those times so much and know how fleeting they will be.
It seems in this case with "WE drink each other dry" that perhaps it's mutual? But I love how this lyric captures that absolute desire to milk each short moment with that person for all it's worth.