When the script is ready, connect your signal to the outside script. That function name will be your 3rd argument. So assuming "mycustomsignal" is the signal you made (1st argument), target is your separate class object (you'll have to attach it to a node, maybe a plain Node2d) and then the 3rd is whatever function you want to call.
func _ready():
self.connect("my_custom_signal", target, "_separate_class_function")