My 2013 Explorer had a wobbly head rest due to someone breaking the headrest guide. Luckily they are inexpensive and can be changed out with just a flat head screwdriver. This works on many Fords but verify your part numbers before buying the replacements. For this vehicle my part numbers are:

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Black: CU5Z-96610A16 BB
Gray ("Stone"): CU5Z-96610A16 BA