I dyed a set or white polymer revolver grips black with powdered Rit dye.
I put enough water in a small pan to cover the grips. heated the water and mixed in a packet of Rit powdered dye, the boiling water dissolves and concentrates the powdered dye. Removed pan from heat and soaked grips in hot dye overnight. Removed , washed them and they are a beautiful jet black color and the dye does not rub off. The dye seems to get down into the plastic... I've shot with them several times the black stays put.
Try brushing the hot dye into the gouge with a small brush , fill the gouge and let it soak in over night . The dye was absorbed by the plastic grips and might color your frame. The packet of dye is not expensive .
Gary