Sinking pedal is a typical sign of master cylinder problem. Any shop that does brakes should be able to confirm if that's the problem.

I wouldn't think it's a brake pad problem. You might need new pads but worn pads by themselves won't make the pedal sink.

The other possible reason is a leak in the brake pressure distributor. I don't know if other cars have these, but the 240s do. It has two brake lines going in and six going out to the calipers, so I call it an octopus. It's located on the inside of left fender wall, pretty much straight down from the master cylinder. Nearly impossible to see from the engine bay, but you can see it if you skinny under the car. If it's leaking I would think you can see the drips - you probably need to look inboard of the tire footprint. Or maybe just behind it?

If that thing is leaking, it will leak faster a few days from now. I had it go bad on two 240s. It started out only needing fluid 2-3 days a week. Eventually got so it needed fluid added 2-3 times a day. When it gets to that point you don't have full stopping ability either, because too much fluid leaks out before you can get the car stopped. Replacement is a pain unless you have a shop lift due to the location.
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Sven: '89 245 NA, 951 ECU, open-front airbox, E-fan, 205/65-15's, IPD sways, E-Codes, amber front corner reflectors. Wifemobile '89 245 NA stock. 90 244 NA spare, runs.