Do I still need to submit this form. I have just changed the corresponding authorship from 1st author to second author. I have not added any new authors or change the authors order.
This form doesn't seem to apply, as the list of authors is the same. Being corresponding author has no direct connection to how much you have contributed, so you don't normally need to justify the choice of who it is.
I would simply have the current corresponding author email the editor (usually there is a way to do this through the system) and ask to change the corresponding author. I have done this without problems in the past.