TaxCode is not a field that you can filter product variant search results on. If you are looking for product variants that are missing a taxCode, you will have to do so manually.
Surely there must be a workaround to get a result of all Products or ProductVariants that have an empty taxCode. Why not just take the results of the following query into an array and then loop through to find all the products without a taxCode. Wouldn’t that work?