If you want to set the eBay category from a custom attribute, you should perform the next actions:
1) Create a product attribute in Magento and add this attribute to each attribute sets in Magento.
2) Fill in product attribute value with a numeric ID of eBay store category. (It should be ID, not the Name)
3) Select the attribute as the source for eBay store category. (Note, only attributes presented in all attribute sets of Magento are available for selection.)
You can see the ID of the particular eBay store category inAccount >[eBay Store tab] by clicking on "category". Also, you can use Refresh button on that page to re-synchronize eBay store categories if they were changed on eBay.