You could use the engine's pause feature, but honestly it seems like a quick fix that might cause some issues down the line. It may be better to implement some form of custom pause.
I needed to pause my player's activity during certain times, without resorting to the engine pause. What I did was create a disable() which disabled their collision, and stopped move_and_collide() from firing and reset the player's inputs on frames that the player_active state was false. If there were any functions that fired in response to signals, I also had them check the player's state before running.
That's only for one node though, it'd probably be more complicated to stop everything, but hopefully that description helps.