Things I've learned and done along the way to restoring bicycles:
"Vulcanite" was the first plastic used for bicycle grips as early as the late 1870's and were found on Columbia and other brand high wheel bicycles. From looking at your photos it looks like Vulcanite to me. If it is wood or this wood was shown in the catalog print, I stand corrected but I want to share what is a fun project if you are handy or know a machinist that can help you.
Vulcanite was also used in the centers of very old bowling balls and still can be found today. I have literally found old bowling balls from bowling alleys that have have had them taken out of service due to damage on the balls and have been in storage for decades. Also they turn up at garage sales.
Once you think you have a very old ball, take a electric hand drill and a long drill bit say about 1/4" to 1/2" in diameter and drill into one of the finger holes until you feel you have drilled about 1/3 of the depth into the ball. Watch the color of the chips from the drill as you go. The outer layer(s) of the ball may be gray or other colors than the black color of Vulcanite you are wanting. If black chips start to emerge from the flutes of the drill bit, stop drilling and feel the chips. If they are rubbery than the center is not Vulcanite. If the chips are brittle then they are probably Vulcanite and you can proceed to making a slicing jig.
You can make a jig to cut the bowling ball in half safely by cutting or purchasing a square plate from 1/2" thick aluminum that is the same length and width as the bowling ball diameter. At the center of the plate drill and tap for a 3/4" or 1" pipe thread and install a "close" pipe nipple in this threaded hole.
Now tap one of the drilled finger holes in the bowling ball with the corresponding pipe thread and assemble tight to the square plate.
Using a vertical bandsaw, place the edge of your plate which is now standing vertical on the band saw table with the diameter of the ball touching the table as well and start cutting through the ball at it's center. Use a low speed as you don't want to create heat from friction of the blade.The object here is to cut the ball in equal halves for easier cutting later. The reason for the square jig plate is so the ball won't spin as if you were trying to hold it by hand and cut it in half which I don't recommend because if the blade catches in the ball when cutting, you can't stop the ball from spinning and more than likely will have a bad accident. Remember the ball is not as important as your fingers or hands!
Once the ball is cut in half, remove the half affixed to the aluminum jig plate and you now have two equal halves that can safely be laid flat on the band saw table. Lay out some lines over the sphere just larger than the diameter of the finished grip size you want to end up with. Slice both halves up so you have some extra material to work with for future grips or make extras for your use or sell/trade them off to other collectors, might as well as the Vulcanite is a dusty and stinky mess and you should wear a mask during the cutting operation and don't want to make a career out of this!
A coarse pitch wood cutting band saw blade like a 4 - 6 tooth per inch blade is best so the blade will not clog up going through the thicker spherical sections and will clean itself as it rolls over the upper and lower band saw wheels. Use your hands to push the material to a point of safety than switch to a push stick.
Now cut the width of these strips you just cut oversize of the grip diameter you want.
You now have square strips that can be cross cut to an oversize length of the grip you want.
Mark the centers of each end and use a 60 degree center drill and drill each end of each piece on a drill press with a table vise to keep the material perpendicular to the drill press table.
These pieces can now be chucked up in a 4 jaw chuck of a metal lathe and the center drilled end can be supported by a live center in the tail stock.
By repeatedly turning the outside to an oversized diameter, you will now have round bar stock that can be chucked in a 3 jaw chuck of the lathe and can be drilled and bored to the handlebar diameter to an appropriate depth or have a through hole for the handlebar diameter. Also any end step shoulders can be made for ferrules and end caps at this point.
You can fabricate a stub mandrel or end mandrels that would support the grip from it's inside diameter and turn outer arced radius to suit what you need.
Filing, sanding and polishing can also be done on the lathe at this point.
Have FUN!
Mike Cates, CA.
PS: Not being a wood officionado, if Gutta-percha is the name of the wood needed, try Tropical Exotic Hardwoods of Latin America in my home town of Carlsbad, California as they carry many species of rare woods. Try to talk to Mitch Talcove (the owner) as I know him from my being a founding member of the California Surf Museum in Oceanside, CA and he collects early wooden surfboards as well and this is how we met. Great guy and if he doesn't have it, he will find it. Their phone number is:
(760) 434-3030