[arcanemachined]

For iPhones, there is a background noise generator built into the phone (in Accessibility settings, controllable from the Control Center). On Android, a similar solution likely exists (one that continues to play even if other apps are playing audio).

You would just need to set one of those up, quiet enough not to be too annoying, but loud enough so that the stereo doesn't think its silent.

Also, there are audiobook players (for Android, at least) that skip over silent sections of the audio track.