The Eeze Bleed is designed as a topper up, but if the reservoir on the master cylinder is full, you'll get a bit of bleeding done with nothing in the Eeze Bleed bottle. So if the cap leaks where it connects to the master cylinder, you don't get brake fluid everywhere.
Sometimes, the traditional way, with an assistant is the only way of bleeding. When you've closed the bleed nipple - get your assistant to sidestep the pedal and allow it to come up with a bang. I've used this technique successfully on a number of cars and most recently, a Land Rover clutch.