No bleeding required with just a pad change
Although it maybe a good idea to bleed them if the fluid is still from 2000
So unless you have a leak or a swollen rubber brake hose, the sinking would for sure be caused by a worn out master cylinder
I say this because the system has not run out of fluid
No air has been let into the system
No leaks are present
The next culprit would be the master cylinder is 25 years old and the seals are worn
So save the bleeding for when you swap out the master you will be able to get all new fluid in there
Don’t buy a cheap reman master cylinder
From this list I would get the ac delco (last one listed) or a raebestos for a little cheaper with ac delco being the best of them available
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