Well, you could try looking in hobby shops that focus on crafting supplies. Sometimes, certain online stores specializing in unique or hard-to-find items might have gum base for Cave Story. Also, it might be worth reaching out to forums or communities related to Cave Story to see if anyone has suggestions on where to find it.
To get gum base for Cave Story, you could start by checking local craft stores. They might carry it or be able to direct you to a place that does. Another option is to search on well-known e-commerce websites. Just make sure to read the product descriptions carefully to ensure it's what you need.
I think you might find gum base in some specialized stores that sell crafting or DIY materials related to confectionery. Maybe check online marketplaces too.