Learn English – word for a location where there is no signal or means of digital communication

In pedagogical terms, we talk about "synchronous" vs. "asyncronous" communication.

In synchronous communication, we're talking to each other at the same time; in asynchronous communication, you may not see what I'm saying as I'm saying it, and you may reply at a later time.

I’ve often heard the term cotton mouth to describe this phenomena.

The Oxford learner’s dictionary labels this as US informal. An online wellness article indicates that the chief symptom of cotton mouth is "a severely dry mouth” and says that one way to avoid it is by limiting your alcohol intake.

I’m not sure how widely recognizable this term might be outside of the U.S., but it might work well as slang in a song lyric. It even has the same number of syllables as hangover, so it might be an easy fit for you.