Getting the client side validations in place to show and hide divs on a page can be a little tricky if it is not something you have done before.
I have an example page that I created that has the type of validation on it that I think you are asking about. I will post the page itself and list the steps that I took here to get it in place.
make sure the form is in place include the divs around the two fields you would like to toggle. The divs must have unique ids for the areas they surround. You will also need to default the divs to be hidden by adding this inline style:
in my example my select list has two choices, only one choice has a value, the other option has it's value set to "".
select your select list in the form, then go to the tag > behaviors panel to apply the client validation. Choose the required/not blank validation. Make sure it is configured for the current select list.
as a response to the required validation apply the show hide layer validation response. Make sure to select the first div as the target layer, and choose to hide this layer if trigger is valid.
Now that you have your first validation/response combo you can add in the second. For this one you will add in another required validation for the select list, then your response validation will be another show hide layer. In this one you will select the second div as the target layer and choose to show this div is trigger is valid.
You should now have a form on the page and have two sets of validations applied to the select list. The first is to check if a value has been selected, if true then hide the first input, the next validation will check to see if the select list has a value and show the second input. Since these validations for show hide reverse themselves when the triggering validation fails you do not need to worry about the alternate states. Attached is an example page of this validation in place.