The ' gunk ' is a build-up of grease so a solvent is required . I use a thimble-full of pure ( artists ) turpentine which is enough for the entire fretboard. Work it around the base of the frets with a cotton bud. Do half , or less, of the fretboard and then quickly wipe it clean with a clean rag. This is to prevent the turpentine from removing the natural oils in the fretboard wood itself. Rub the fretboard dry. When all of the build-up has been dissolved and wiped away rub pure (artists ) linseed oil into the fretboard with a fresh rag. Let it dry naturally for an hour or so and then rub the fretboard dry again with another fresh rag. By that time the oil will have fed the fretboard surface to preserve it. Lemon oil is just as good as pure linseed oil- but maybe smells a tad girly.
There will be, no doubt, those who turn pale at the thought of putting a solvent on their fretboards- but I've been using turpentine for years with no problems whatsoever. Fortune favors the brave.