Mineral spirits and cotton swabs and small brushes, like baby's toothbrushes. Also manicure sticks.

Swab on the mineral spirits with a soft cloth to soften the gunk, and clean out the crevices with the tools.

You might not want to remove all the gray gunk. I think
It's similar to the black tarnish in silveware. A little bit of background color to accentuate the patterns. I'd try buying some Pledge wipes and usen them to spiff up this piece. Good luck.

But would mineral spirits take off the wood's finish? Not sure I've used those before, but it's worth a try if the finish doesn't get damaged.

jannie, the layer of light gray gunk is very noticeable in the dark curls of the oak pieces. It looks as tho I haven't dusted in 50yrs., tried scratching it with my fingernail and the stuff won't budge. I'm wondering if I'm seeing it now because the room has been remodeled and there is more light in there now! ha.

Just had a thought, in the past I've used Murphy's on a damp cloth once in a while to wipe the headboard down, suppose it ruined the finish? If that was the case, the rest of the headboard would be gray too tho. Thanks for the suggestions.