I know this thread is old, but I just stumbled across it and felt like I needed to add my interpretation as well.

I've never thought this song is about suicide specifically, but I absolutely feel it does refer to death. More focused on the awareness of it's imminence and that it is close at hand more than the method it will arrive.

There's a need to calm whoever the subject is singing to. It feels to me like a soothing explanation that death is coming, but the subject has made peace with it and they want you to know it's going to be alright once they're gone.

This view of this song has helped me through some very difficult times in my adulthood. Death becomes a more common part of life as you age and being able to listen and mourn with a song of this caliber is infinitely cathartic and I will always be grateful for Tom Waits and his brilliance.