The pedal is returned to the home position only by spring tension. With the engine off and one of the PB hoses disconnected so all the reserve vacuum is out of the system, if the pedal does not return via the spring you can be fairly sure something is misaligned or binding. It could be some mechanical issue with the carpet or pedal & bracket, the assembly lube could be sticking, or possibly the small clip that holds the upper spring retainer cup to the hydraulic piston came off and the spring is not under enough tension to push the power piston up. One poster even found his spring had been rusty and finally broke in two but a broken spring is a rare condition and not as likely as the other causes.
If all seems normal without vacuum, then hook the vacuum back up and if the problem happens there is something in the vacuum or valve mechanism that is allowing vaccum to leak into the power side and pull or hold the piston down. You did not mention a year but if it has the rubber poppet valves, one could have dried or cracked allowing a leak. If it is the first version with the spool valves or has the firewall mounted breather make sure no problems are in the hose or breather and air can get back into the unit. On canister mounted breathers make sure nothing is blocking the two holes under the air filter. Also make sure the vacuum is connecting to the proper port on the two hose units. Another possibility on either unit is a felt cushion on the cover has loosened or been installed incorrectly and the piston is not able to completely return to the up or home position to allow the valve to close. If that is the case the brake might think it is starting to be applied and a tiny bit of vacuum is getting into the power side of the booster holding it in position.
As to how you know if the booster is working, believe me you will know. With everything working properly, just a light push on the pedal with your toe will slow the car to a stop. Pushing harder as you might do in a panic stop can be enough to get you up close and personal with the steering wheel or windshield. If the booster is not working you can all but stand on the pedal and consider yourself lucky if you slow down within a reasonable distance, let alone stop. With the 1:1 pedal ratio, the amount of pressure at the wheel cylinders is not multiplied by mechanical advantage so without the booster, pressure at the brake shoes is dependent on how hard you push the pedal and a couple of hundred pounds doesn't do much.
Check out this commercial at about the 40 second spot for a demonstration of the normal brake operation. https://www.youtube.com/watch?v=eMgriMYCtNc
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