Fully synthetic oil in a wet clutch gearbox will be fine, provided that it does not have friction modifiers added. All motorcycle specific engine and gearbox oils do not have the modifiers that cause the clutch to slip.

I recently put in genuine Honda four stroke GN4 oil in my NSR gearbox (it took 800ml). Took it for the first ride today, and the shifts are incredibly smooth. Previously I was using shell gear oil and for some reason it was very notchy.

Procedure for filling with oil - just pour it in. Put 700ml in to start with then hold the bike upright so that it is balanced and check the level with the dipstick while it is upright. You only dip the dipstick in the hole - do not screw it in. Add oil until it is filled to the top mark on the dip stick.
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MC21 Honda NSR250. TYGA 300 conversion.