King,
When I finish a fret work clock I do my finish prior to assembly or you will not get all of the intricate inside areas. What I do is take a paint roller tray and a liner, dump a half can or so of Danish oil into it and submerge the pieces into it one or two at a time, sometimes more depending on the size. If they are large you can lay them down and rock the pan like you are panning for gold. I leave them soaking for a few minutes and lift them out and wipe with a soft cloth (cut up t-shirt - fold it though so no cut edges of the shirt are visible so you do not leave little bits of cotton) Then I set them down on a table covered in brown painters paper, wiping them down with a clean cloth every 30 minutes or so on both sides about 6 times or until the finish looks even, the brown paper will pull excess oil out of the very fine areas. I repeat this entire process 4 or 5 times. It is time consuming but worth the effort as all surfaces are evenly coated, no 'white' spots. When complete (I allow 4 days drying time) I use 0000 steel wool to LIGHTLY polish. Prior to assembly I use a shop vac with a brush attachment to remove any fibers from the steel wool that may have been left behind and then inspect under a lighted magnifier and tiny tweezers to get anything the vac may have missed. When polishing I cannot emphasize enough the need to be very careful not to snag the steel wool on the delicate pieces, hence lightly and carefully always paying attention to the curve of the cuts and any sharp edges. I then assemble with rhino glue.
There are different methods and I am sure you will get other suggestions but this has worked very well for me in the past. A clock that I finished like this won best of show in the state fair and I know that finish is part of the judging.
What ever method you use, take your time, you have put hours of time cutting it and the finish will really highlight all of the excellent cutting you are obviously doing. You can see examples of this finish at
Barefoot WoodworksPhoto Album The Grover Irish clock done in Cherry and Walnut is the one I am referring to.