Hi Appa's Papas,
You were a help in suggesting I check to see if the Timer's working. From what I remember at first it wasn't and then I got it to work on its own. Thing is, though, even though the Timer's working, it won't play the AnimationPlayer.
I'm not sure how to do what I'm trying to do, but I went and asked a question on the Godot Community. Hopefully someone there will know what to do. If not, well, then I may have to do something else or go and have the scene change to another scene where the character spawns in or near the same area and have the Timer start when the new scene starts.