Custom product form - How to only make it appear when having selected a specific variant?

Hello,

Is there a code to customise the product form so that it only appears in the screen if the customer has clicked on a specific option/variant? For example, I made a "personalisation" option button. If the customer selects "yes" for "personalisation", I want the form to appear so they can specify details about the personalisation option. However, If the customer selects "no", I don't want the form to appear as it would be very confusing. 

Would really appreciate some help! 

Thank you 

No. It will always appear.

@paul2009 So there is no way for the customer to write their details for an order is a specific variant is selected?