You can do the following:
1 - Fill the crack at the bottom with a very thin coating of Super Glue. This will bond the bare wood to the edges of the plastic pearl and prevent the split in the plastic from enlarging any further.
2 - Go to a quality arts/hobby store and purchase several small bottles of acrylic paints in colors approximating the pearl (flat white/egg white/luminescent white, etc.) along with a few inexpensive thin brushes with plastic bristles. Total outlay: from $10- $20 plus or minus.
3 - Carefully mix/match the paints on a separate piece of white or neutral gray paper to closely approximate the general appearance of the pearl. Usually the paint will appear slightly darker when dry. Don't worry about 'absolute perfection', as a broad white surface with no bare wood showing below split plastic is "seen" by others as a fully intact white surface. Usually old drums have acquired varying shades of discoloration, stains, scratches, etc. anyway, so your artistic goal is to paint in a little more to fool the naked eye into seeing "a white pearl finish drum". [tip: you can purchase 'clear gloss acrylic' and mix it in with your luminescent white colors, shaded with various small amounts of "off white" to arrive at a shiny gloss white pearl appearance almost exactly matching your drum.] Acrylic paints allow for a complete cleanup using only water so you have a little room for error if not happy with the first attempt. Usually you can clean it all off within the first hour if a mishap occurs or if you need to further mix and match your paints.
4 - Use a brush to apply your final choice of color mixed paint into the split. Sometimes it's most efficient to allow a small amount to "drip" into the crack and let gravity spread it to fill the split. Apply one thin layer at a time, allowing each layer to fully dry before applying another. Build up the paint patch higher than the surface of the surrounding drum surface, as 'shrinkage' usually occurs as the paint cures and dries.
5 - Then use micro-sand papers to take the surface down close to level with the rest of the surrounding pearl wrap.
6. Follow up with Novus plastic polish or a similar product to remove the hairline scratches.
6 - The result will not be factory perfect but from two or three feet away should be visible only to you when the entire set is assembled.
This method was suggested to me years ago by a professional luthier. I've used it many times on vintage drums including on sparkle finish pearl plastics, with good results. Unless I point out to someone the "scar" they usually will not see it. Of course, the drum is never of the same resale value as would be if factory mint condition, but if the goal is to "repair" a surface blemish on a quality vintage drum without the hassle of doing a complete pearl removal/re-wrap then it's both an available option and a relatively inexpensive one.