Editing Multiple Tracks, Removing Silence from each

Currently I record a podcast each week with another guy. We each record our audio on our own computer, then he shares his exported audio. I import it into my audacity and begin editing. I have found that the best way to get the clearest audio possible is to delete all of the sections of each track where one of us is not talking but still leave the space in that track so that it stays synced to the second track. It is incredibly tedious and time-consuming. I guess one solution would be for us to mute our mic while we are not talking but clicking the mute button on and off also adds a click I would have to remove manually.

Truncate silence won’t work because then the individual tracks won’t sync up correctly…

Is there a simple way to do this without having to go and manually delete every single gap from both tracks?