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Common sense here man. If it's holding pressure with engine off and you fire engine up and pedal goes down and won't pump up... It's a vaccum prob.

Eaither the vac hose from carb to booster, or the 1 way check valve on booster where line hooks to, booster bad or engine is not making enough vaccum to run the power brakes (common on engines with large aftermarket camshafts)

Checks; Weak Brake Lines, Bad Master and/or Brake Cylinders, Weak Brake Booster.

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Change the plunger in the master cylinder, it is bypassing fluid internally and not allowing you to have stable pressure. I would also change the brake lines too, cause the will breakdown internally and cause brake fade (pedal going to the floor).

check the brake cylinder then if ok check to see if power booster is leaking

Master cylinder, It;s old and tired.