There is no tool in Premiere Elements for adding timecode to your video.
I have heard of people using this third-party plug-in. But I have no experience with it and can not guarantee it will work for you.
I also believe that DVDate can add a TimeCode Effect.
I use either Premiere Pro, or After Effects, both of which offer a TimeCode Effect, best applied to a Transparent Video on a Video Track above, so I have not needed to explore any 3rd party apps.
Good luck, and let us know what you find, and what works best for you.