It may feel dry to your hand, but it'really not. Oil will never dry.

gojo original with out pumice is what i use to clean cabinets and then i polish them to full luster with good ole fashioned johnson paste wax.

This is what's called "THE TREATMENT".

.

Got the Howards restore. Did zip for me. It definitely not a restore in the least. Waste of money.

Howards did not work on this radio, but was stunning on another old dryed up wood radio. Howards just will not cover light areas where the original stain is gone.

Use Old English Scratch Cover for dark wood.
You'll likely need to clean it again so that nothing keeps
the Old English from getting to the light colored finish.
You can use several coats to hopefully get the darker color
you seek.
Buff it off with a clean paper towel several times until the
paper towel stays clean after each application.
After you get it to the color you want let it dry for a few days
and then apply a good paste wax like Johnson's Wax.

I have restored a 28 Majestic with pledge that looked like it had just took a dirt bath. Far worse than yours. It came back to a beautiful smooth and glossy finish with just spray on wax. I figured that if multiple coats of wax over a couple of weeks didn't bring it back I can always sand it down after.

I have a Zenith 9S367 that every inside 90 degree angle was white with the lacquer pulling away from the inside corners and whitish dry scratches all a round. I found a Winwax stain that was very close to the color. Applied the stain and then used french polish to seal it. It looks great! I hope what ever you choose that It comes out the way you want it to.