The brake pedal now goes very low when pressed, and it takes very little force, but the brakes work. A single, partial "pump" of it helps a lot, makes it almost normal again. There is no sign of leakage, no rotor/pad problems that I can see, and plenty of fluid in the res., nearly to the "Max" mark. There has been no recent brake work, not in 2 years, and it was well bled back then, so shouldn't be air. Could this be the master cylinder getting close to failing?

For what it is worth, for a long time the brakes have worked well, but when first stopping, after a few seconds, the pedal would go softer and lower all by its self. A quick, single "pump" would restore pedal height.

All I can think of is the master cylinder. And the car is old enough, will be 19 years next month and about 300,000 miles, that it may have wear or worn piston seals.