There is no “headphone option” in settings, but this is what finally worked for me on my 10.5” iPad Pro:
# I cleaned the headphone jack with a stripped-down q-tip and 99% isopropyl alcohol. A tiny bit of dirt came out, but did not fix the problem.
# I removed all cotton from the other end of the q-tip, and trimmed opposite sides of this end to create a flat “wedge” shape narrow enough to fit (snugly) into the lightning port. I saturated this end (mostly paper at this point) with 99% isopropyl alcohol and probed the lightning port repeatedly, making sure to cover all corners and sides. The cardboard wedge end of the q-tip was noticeably discolored:[br]
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As soon as I finished step 2, the iPad left headphone mode and the speakers started working on Music and YouTube videos again!