Record input twice, muting at certain times for one

Sorry if the title is a little convoluted, it’s the best way I could describe it. What I want to do is to record from one input into 2 different tracks at the same time and being able to mute one track at times while the other stay recording.

The task, in the way that you describe it, is not possible in Audacity.
What are you actually trying to do?