Is it possible to make pause game working with remote play?

[AkazaRenn]

This is for Steam Remote Play (LAN streaming). What I want is that when the streaming client switches out of a game (open overlay, go to home screen, etc), the game that is running on the host pauses until the client comes back. It'll be really cool if that would happen. However, I'm not sure if Steam passes any kind of signal when the overlay is opened from the streaming client, thus it may be totally impossible.

Current behavior is that, with Pause Game installed on both host and client, they do nothing. When an overlay is brought up, the music is still playing.

If it's not doable, as an alternative, maybe we can pause the game when the remote play client disconnects, or bring up the overlay when it happens to trigger the pause, so it doesn't immediately restart when the client reconnects?