I don't remember how I implemented the workaround for shaders not pausing in no signal. I think it would be useful to add to these notes, so here's what I had written:

var scaled_time: float
const HOUR: float = 60*60

func _process(delta: float) -> void:
	if not get_tree().paused:
		scaled_time += delta
	while scaled_time > HOUR:
		scaled_time -= HOUR

	RenderingServer.global_shader_parameter_set("SCALED_TIME", scaled_time)

In order to work, a global shader parameter with the name SCALED_TIME needs to exist in the project settings and this code needs be added to an autoloaded singleton. In the case of no signal, it is part of the GameState autoloaded singleton.

I checked why I implemented a rollover of one hour, and it seems like I probably did it this way because that's what's done by default for the TIME built-in.