There is a chance that the fiberglass parts are gell coat, with the color in the resin. Stuart
Molded fiberglass, with gel coat, is becoming a thing of the past, (except in boats), in favor of sheet molded compound, (SMC), PVC, ABS, and polypropylene plastics.
SMC has some fiberglass strands in it, but does not use fiberglass resin. Corvettes which most people think of as old fashioned molded fiberglass, have actually been made entirely of SMC since the 1984.
How can you tell which you have? Check the inside, or underside of a piece. If it is rough, and strands of glass are apparent, its fiberglass, which is usually gel coated. If its smooth, and the bare plastic is of a gray color with faint swirls in the pigment, it's SMC, this is painted. If it's rigid, smooth on the inside, and white or black on the inside, it could be ABS, or PVC, which is used raw, and painted. If it's the same color on both sides, smooth, or lightly textured, low gloss, and somewhat flexible, it's usually polypropylene, or similar plastic, cast in color, and not painted.
If its polypropylene, raw PVC, or ABS, products designed for painted surfaces will have little to no effect. Mechanical buffing can actually melt them. Your only options then, unless you use extreme care, are vinyl cleaners and shine products.