So I went out and removed the old trim from under the gauge cluster and I think I have some idea of what a previous owner has done. It looks like they peeled off the veneer from the original trim piece, leaving the base wood in place. Then they got another piece of trim wood, removed the mounts from the back, broke off the side wing, and glued it in place over the original base wood.

I can't fathom why someone would not take a few minutes to do the job correctly. It only took me just under two hours to salvage every piece of wood in that 380SE and that included taking off all 4 door panels, CCU, and other odds and ends. It only took me an hour to swap in the new piece and the passenger vent piece.

I'll post a picture of the old trim so y'all can laugh because it really is so sad, you can only laugh.

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1991 F250 super-cab 7.3 IDI. (rebuilt by me) Banks Sidewinder turbo, hydroboost brakes, new IP and injectors.
2003 S430 - 107K
1983 300SD - Tanoshii - mostly restored ~400K+.
1983 300SD - Good interior. Engine finally tamed ~250K.
Monark Nozzle Install Video - http://tinyurl.com/ptd2tge