Sounds like guide pins to me... replace the caliper assembly and that should solve the problem. Replacing the guide pins will help but will not totally eliminate the issue. Seems that the pins and the caliper like to wear each other and the holes open.
Also, rotors don't really warp... there is a lot of discussion on this online and a it's more of a myth than anything. Personally, i don't believe in turning rotors.
Warped' Rotors Myth - Correctly Service Brakes: Runout, Disc Thickness
Good point on "Slide pin" (AKA guide pins).
Although I've done some very raunchy caliper up to 350K miles, lightly hone out slide pin holes to clean up. I did not have issue with pulsating pedal in any I've done. Also keep in mind the rotor puts pressure on pads in one direction at a time. Some minor movement in that direction of rotor in pads within cage and cage on slide pins is normal. Bigger issue is with slide pins, is sticking, causing pad to rub excessively on rotor after brake pedal released.
Whether warped, uneven pad bedding material deposits on rotors' disk surface or variation in thickness turning corrects. We just call it "warped" That is a debat that race car engineer feel they've answered as "uneven pad material deposits". Bad bearing or uneven hub mating surface for deposit not cleaned off hub or brake of drum back is different issue. Uneven torque or pattern of lugs tightening is not really issue with bending disk/warp in the 100 design, but proper procedure should always be followed.
I did have one rigs' front brake pedal pulse so bad the steering wheel pulsed. Those brakes were fairly new pads & rotors replaced 20K miles earlier with OEM pads and aftermarket rotors, by a "Toyota specialist shop" in Denver. I suspect they didn't bed the pads, than PO got in a drove as normal braking and stopping with foot on brake at first stop he came to, creating uneven heating on rotor. Pulsing didn't show in my test drives, as I didn't overheat the brakes. I don't use brakes to control downhill speed, it's just foreign for me to use anything but gearing (engine brake) on downhill.
This driver was using brake to control speed on the down hill (bad practice) overheating brake pads & rotors. This brought out a "warped" rotor condition that was present but undetected until then. He took to Toyota Dealer which turned Disk (rotors) on the rig and kept old pads, problem solved.
I do believe in turning rotors and do so nearly ever pad replacement if used rotors
That said I just had a shop mechanic (of 40 years) tell me; how on his personal rig he put all new rotors and pads. He used the most OCD bedding/seating procedure I've ever heard of, parking and let cool for 5 hours before using brakes to come to a stop. He had issue with pedal pulse. He assumed run-out okay since new rotors, so he did not do check (I don't either shamefully) , trusting their not warp. After looking at everything but run-out, he checked. Sure enough he had one warped rotor. He convinced they were warped. Replaced, with second set checked run-out, rebedded/seated all was good.
