While braking continuously on a long shallow incline, the brakes will suddenly grip harder in a predictable way, jerking me forward a little and braking harder from then on. Like it switches from one deceleration rate to another. Is this the transmission switching to engine braking? The brake pump turning on? I don't think it has anything to do with the pads or rotors themselves.
Update: I watched the tachometer this time and it jumps up in RPM when the braking gets harder, so it's the gear shifting. Is it supposed to affect the brakes suddenly like this?
Yes, the transmission downshifting is adding engine braking, in addition to the constant brake pressure you are applying. This will cause the car to slow down faster, as if you had pressed the brakes harder.
I watched the tachometer this time and it jumps up in RPM when the
braking gets harder, so it's the gear shifting. Is it supposed to
affect the brakes suddenly like this?
No, it is not affecting the brakes but it is certainly affecting the deceleration as the engine braking is more powerful in lower gears (the rpm-to-speed factor increases, thus giving the engine more relative brake power). This will feel like as if you've suddenly pressed the brake pedal harder but has nothing to do with the braking system.