I followed all the steps described in the instruction manual, but it is impossible to connect vinyl in external mode and it does not work as TIME CODE either, what is the solution?
What do you mean by "vinyl in external mode"? If you mean external mixing mode that should not be used with the s4 mk3. Do you mean live input deck?
If you are on mac os, make sure that traktor can read the microphone https://support.native-instruments.com/hc/en-us/articles/360000471958-macOS-Dialog-App-Name-would-like-to-access-the-microphone
And in input routing, when you play a vinyl (normal or DVS) can you see it getting a signal. Show us a screenshot of your input routing settings.