Spells are written in a way that is easy to read ambiguously - whether "you" in the description refers to the player or the character.
I generally take the latter, which means that the spell must use an in game, in-narrative event as its trigger. Death saves are not events in the narrative, they are game abstractions, and I wouldn't rule them to be a valid trigger.
On the other hand, I'm not trying to screw my players over - if the intent is to make sure the spell goes off when the character is on the verge of death and not unconscious for some other reasons, then, "Fall unconscious and dying from wounds," would do the trick.