No, use lemon oil for rosewood fretboards
Gibson SG Standard with Bare Knuckle Riff Raff and Stormy Monday
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Fulltone OCD
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Fender Bassman '59 Reissue
Gibson's polish is for cleaning nitro finishes, it's not for fretboards.

To clean a rosewood fretboard, you need to consider the condition it's in, the quality and specific species of the rosewood, the use it gets and the nature of your skin. If the rosewood is looking dulled and feels dry under your fingers, if you don't use the guitar much, if it's often left out in sunlight or in heated rooms and if your skin isn't naturally very oily, a small dab of lemon oil, applied to an inkless microfibre cloth and rubbed lightly over the fretboard (though try and keep away from the fretwire itself and the back of the neck, unless the whole neck is a one-piece rosewood neck) is usually all that takes to give it new life.

If the fretboard is simply dirty (but not actually dried out) then all you need is a dry inkless microfibre cloth. Lightly rub over the dirty areas using a soft circular motion, and any lose dirt should come off easily. If there are more stubborn marks, it may be best to very, very lightly dampen the cloth with the most minimal dorp of lemon oil (with lemon oil, it's always best to use too little than too much. If you don't use enough, you can easily just go over it a second time - if you use too much, you can ruin the fretboard and you can't undo the damage).

Some high-grade rosewood fretboards and necks, when stored properly and played regularly by someone with average to moderately oily skin, can last three or four years without needing any kind of cleaning or oil treatment. Other, cheaper rosewood, especially that which is played by someone with very dry skin and that is subject to high heat or sunlight, may need to be treated with lemon oil every three or four months.
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