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Unless someone has modified something (unlikely), the connection is chromed steel in nylon, no general role here for penetrating oil. You should be able to release it by pulling up. Diagram of the headrest
Picture of the seating locations for the headrest in the mechanism - nylon 'wings' on the side of the mechanism Picture shamelessly stolen from another thread.
Thx for the pix and info. Looks like I just need to pull harder, or leverage the headrests out???