Microphone not showing up as input device in settings, only in pavucontrol

For whatever reason, the interface isn't being seen as a source by PulseAudio. It needs to be manually configured via forced loading and detection. The steps are as follows:

1. Use the command:

   arecord -l
   

   and note the card and device numbers.

2. Open /etc/pulse/default.pa as root in a text editor.

3. Add the line:

   load-module module-alsa-source device=hw:c,d
   

   where c is the card number and d is the device number.

4. Below that line add:

   .ifexists module-udev-detect.so
   

5. Save the file and reload PulseAudio. This can be done from command line with:

   pulseaudio -k ; pulseaudio -D
   

This should force detection as an input source. To see the process used to verify solution, see the comments under OP. To find out more info about troubleshooting issues in PulseAudio, see the Arch Linux Wiki for PulseAudio/Troubleshooting.