You can indeed pan on recording or "mute recording on alternate tracks" as you originally put it.
It can be easy, or difficult, depending on the software and your technical knowledge, but logically, what you need is this:
Input(1 Ch) -> [Method of splitting/fading between two channels] ->
Recording Tracks (2 Ch; where Ch1 -> Out L and Ch2 -> Out R)
Then on playback, you will be able to pan L/R as you desire.
So… basically you need an input panning control. And as this is not often required, you would need software with good routing capabilities.
Audacity
I tried this in Audacity, and as it's just a simple audio recorder/editor, it is very limited in routing capabilities. The real-time effects looked promising - it seems all you need is an effect with a pan control and then record to a stereo track - but not only did the panning not work, but none of the effects worked in real-time anyway.
Cubase
As I'm away atm, I tried it on a Cubase 5 install I have on my old laptop. So anyway, this is how I did it in Cubase 5 using the free ASIO4ALL ASIO driver (it should hopefully transfer to other software):
- Firstly, I created two mono input buses in
Devices
-> VST Connections
-> Inputs
called Mono In
and Mono In 2
, both using the same input as a source (I used my laptop mic in this example).
This will create two input channels in the mixer by the same names

- I then created two mono audio tracks. On the first, I set input to
Mono In
and output to Left - Stereo Out
. On the second, I set input to Mono In 2
and output to Right - Stereo Out
.
So the first track will output it's recorded signal to the left channel and the second to the right. Simples!

- I then Armed both tracks and recorded. Then, using the mute buttons on the channels
Mono In
and Mono In 2
on the mixer, I could effectively switch between left and right channels while recording.
(I also renamed the channels and tracks to make it easier to understand - Mono In
=> My Lines
, Mono In 2
=> Other Lines
, Audio 01
=> Left
, Audio 02
=> Right
)

Furthermore, you could probably create a macro or key command that would allow you to make the mute button changes with simple keystrokes.
So there you go, one way of doing it. When exported, this will create a stereo file that you can pan/mute L or R on playback exactly as you wanted. You should be able to transfer this or a similar process to other DAWs with a little bit of knowledge.