Bill,
It's the booster - I have experienced this multiple times over the years with cars I have bought/sold. Either the diaphragm failed due to being old rubber or there is a leak out the back of the master cylinder into the booster and the fluid attacks the diaphragm, although this is less likely with DOT3 fluid.
A leak would not be immediately evident as the fluid gets sucked into the engine and burned in the combustion process. The suggestion to check the rear wheel cylinders is also good advice.
My recommendation is to have the booster rebuilt. You can check the back of the master cylinder for a leak while the unit is apart. Here is a good source for booster rebuilding, I have used them several times with good results:
https://www.powerbrakebooster.com/
It's the booster - I have experienced this multiple times over the years with cars I have bought/sold. Either the diaphragm failed due to being old rubber or there is a leak out the back of the master cylinder into the booster and the fluid attacks the diaphragm, although this is less likely with DOT3 fluid.
A leak would not be immediately evident as the fluid gets sucked into the engine and burned in the combustion process. The suggestion to check the rear wheel cylinders is also good advice.
My recommendation is to have the booster rebuilt. You can check the back of the master cylinder for a leak while the unit is apart. Here is a good source for booster rebuilding, I have used them several times with good results:
https://www.powerbrakebooster.com/