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If you have a good high pedal with the engine off and it drops with the engine running, it does sound like air in the system. Make sure you don't have a flex hose that is ruptured and stretching under pressure. It's not a vacuum problem. The booster is merely adding pressure and exposing the problem that's already there.
When your bleeding, have the person doing the pumping observe hour much pedal drop there is as each wheeel is bled. The one that drops the least is likely where the problem is.
No it doesn't drop all the way to the floor. I drops to the second set of brakes. It's a dual system and your hitting the second system. The amount of drop to get to the second set is an indicater of how much pressure you had on the fluid before opening the bleeder. For instance, if the pedal only drops an inch before hitting the other set, it would indicate you hadn't built much pressure and that's likely where you air is. If the pedal drops considerably when the bleeder is opened, chances are the side of the system is OK. Did you understand that?