The tax rule will only trigger if the conditions in the rule are met first. Since the conditions are just looking for a particular session variable to be set and the value is not being set this tells me that your recordset is not working properly. When I check on your page it looks like you are filtering the recordset on this value:
If the county select list is named countyid then you should update this to be the posted version of this form element like this:
If your county select list has a different name then you will need to update this to reflect the name of your list.