(Besides it being a catchy song, and the stalkerish aspect)
Interpreting it as "I'll be watching [over] you", as if it's someone who died is singing it.

Enya also liked the "I'll Be Missing You" song sampling/inspired by it.

Enya's grandparents passed away at some point in the late 70s/early 80s, and she does have a couple of songs, Smaointe and On Your Shore, which refer to her grandparents.

She possibly found Every Breath You Take relatable to the idea of her grandparents watching over her ๐ even when the family seemed disappointed in her for leaving.

