I believe the majority of the brake boosters fail when the diaphram leaks.
If it's really bad you can hear the air hissing thru when you apply the brakes.
Some of them leak so badly it shows up as a large manifold pressure leak.
A vacumm 'leak down' would be a valid test for this.
Pressure testing would probably be testing in the wrong 'direction'.
Vacumm testing is the way to go.
A vacumm hand pump with a gauge on it can be bought at most any of
the chain part stores.
The booster has considerable volume so you'll be 'pumping' on it for awhile. But after you get it pumped down to around -10~-14 PSI it
should hold without leaking down.
If it doesn't hold ANY vacumm, it's definitely bad.
Don't apply the brakes while you're doing this test.
I usually replace MC's when they leak but you could take yours apart and replace the seals in it if you were inclined to do it.
I'm a little spooky about master cylinders (don't know why) so at the first sign of one giving trouble it's outta there and a new one goes in it's place. The master cylinder (or any other brake component) is a major safety item so I feel better with new ones but there's no reason you couldn't repair your old one.
To test the MC, apply constant, considerable pressure to the brake pedal. If it doesn't feel solid as a rock, the seals are leaking. If it slowly moves down under the pressure, it's bad. If fluid is getting out of it anywhere, it's bad.
Make sure there are no OTHER brake fluid leaks when you do the 'leg' test. A leak anywhere
will allow the brake pedal to slowly move down.
Brakes aren't something to experiment around with. They are a 'do it 100% right' or take it to a shop kind of thing.
That doesn't mean you can't fix them. It just means to be honest with yourself about your capability to do so. Your life (and the lives of others) is truly in your hands when you work on brakes so there's NO 'almost right' acceptable when you're working on them.
Good luck with it and 'good testing'.