Look at the headstock exploded view in the 10F parts manual (10L-6 or similar) for a general idea of what it looks like. On your headstock, there should be a hole in the top of the casting above and centered on the hole that the pin sticks through. This hole extends below the pin and originally at least contained a spring and ball.
Soak the pin and hole with Kroil or equivalent overnight. The original 10-42A has a hole drilled across it and a groove pin installed in the hole after the index pin is installed in the headstock. This keeps it from coming all the way out of the headstock. If what you are calling a home-made pin has that, it must be removed first and then the pin rotated until the groove pin hole is horizontal before you pull the index pin out of the headstock. Be careful not to lose the ball, if present.
Whether the index pin is home-made or original, after soaking overnight I would use a C-clamp and a couple of short pieces of aluminum round bar to break it loose. The outer one should be a little longer than the index pin with a hole slightly larger in diameter than the pin drilled through it. The inner one should initially be about 1" diameter by 1/2" long with a 1/8" hole through it. Those plus the C-clamp should break the thing loose. If you still can't pull it out with your fingers, replace the inner one with a short rod just slightly smaller in diameter than the index pin, with a 1/8" hole in one end deep enough to contain the 1/8" diameter pin on the nose of the index pin. There may be clearance problems between the C-clamp and the bull gear that you'll just have to figure out. You may be able to move the bull gear, pulley and small spindle gear a little bit by loosening the set screw in the bull gear and those in the collar next to the small gear.