No need for separate timelines. Put the first two clips on the timeline, select both then click on the
Sync by audio button that will appear above the timline.
Now trim them so they both start at the same time, then move them back to the first 2 tracks. Add the 3rd camera clip to the timeline and select one of the existing clips to sync with, then trim the 3rd clip to match the second and place them both at the start, aligned with the first one.
Pick one track to use for the main audio, then click on the eyeball icon next to the speaker icon to mute the other tracks. In the example below, I'm using the Track 2 audio and have muted Track 1 (and 3 if I had one).
The you'll want to use the Split tool with no clips selected to cut all of them each time you want to change the active camera
To switch between clips as the video progress, you have two basic options. In the above screenshot, you can see that I've dragged the Opacity line down on the 1st and 3rd sections of the Track 2 clip, which will let the content on Track 1 show. The opacity is at 100% in the middle clip on Track 2, so that will be the content in the produced video.
There's a second option that might be easier, and that's to leave all the clips at full opacity and simply delete the ones you don't want. You'll have to first unlink the main audio (or use a copy on a lower track but with the video disabled or with the opacity set to 0) so that your edits won't affect the audio in any way.
Then you'd simply delete any of the lower tracks that you didn't want so the next-highest track would be visible, like this:
Hold down the Shift button when pressing tehe Delete key to prevent the traling sections from sliding leftward when you remove the unwanted sections. If you make a mistake here, simply drag the left or right edge of the same clip to restore the missing section.
It might sound com,plicated to lay everything out here in text, but the process itself is pretty easy to work with even though it's not as easy as the MultiCam Designer