when a form posts, the information is available only while the action page is loading. Once the action page has finished loading or redirects to another page, the form information is no longer available.
since your page at sell_your_vehicle03.php posts to itself, then redirects to the sell_your_vehicle02.php page, the form data is lost when the redirect occurs.
using the session variable is the only way to be able to pass the value between the two pages.