iPhone 16 Pro Max Volume Up button not working after a drop (still clicks)

You, will likely have to open it to reseat or replace the flexible printed circuit (FPC) cable with the power and volume buttons on it. Replacement is difficult because you must remove the motherboard entirely.

Yes there is a technique to the 15 Pro Max and if you haven't used an iPhone in a while you'll find the screen connector has switched to the left side of the frame.

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iPhone 15 Pro Max

The flex cable that the volume and power button are on can be reseated once you have all the metal connector cover sheilds carefully removed from the logic board. I and not sure of the top of my head exactly which Lego style connector is the power/volume, therefore my recommendation is to reseat all of them carefully and gently a properly seated connector will give a very soft and stuble little clicky tactile feedback.

Be careful of the black foamy rubberized cover compound this can be scraped into a connector by accident easily pay close attention none ofadhesive-like material like matieral is stuck between the gold contacts. It can be removed easily with very fine tweezers.