I've noticed that the music for the mysterious stranger is louder when he is closer to you.

I noticed that sometimes I hardly hear the music and sometimes it's quite loud. Then once, I was scrolling around when it played and it got louder as I moved and low and behold I stumbled on the stranger in my path. Now if it's fairly loud, I know he is somewhere close and not at the other end of the vault.

Better than that. If you're playing with earbuds or headphones (i.e., on Bluestacks), the sound seems to be directionally located. You'll hear it to the left or right, vaguely up or down, and at different volumes, pointing to where Stranger is hanging out.