Premiere Elements 12 and 13 are standalone programs. If you install Premiere Elements 13, you do not need to deactivate/uninstall 12. Just use one program at a time. In 12, you should be able to deactivate the program in an opened project's Help Menu/Sign Out. I am strictly an Elements Windows user and that is the Windows way, assumed Mac way as well.
It is always a good idea to finish projects started in an earlier version in the earlier version. There is no guarantee that the earlier version project file will open in the later version program. It probably will, but no guarantees. If you do this, work from a copy of the earlier version project as a safety net.
Do not move, delete, or rename folders/files that were imported into a project after the project has been saved closed.
If you have any doubts about project file links to source media, then archive the version 12 project involved...File Menu/Project Archiver/Archive Project or Copy Project options. I would go with Copy Project option.
Please let us know if any questions or need clarification.
Add On....Consider leaving 12/12.1 installed until you are convinced that you no longer need it after a workout of 13.
Thank you! Everything went smoothly.
Thanks for the great news of success. Great job.
Best wishes as you move forward with your Premiere Elements 13 projects.