I don't think it is possible to connect an external microphone.
The 'connectors' you have are an HDMI port (only allows output), a USB port (some degree of input/output), the SD card slot (dumb output), and the ability to load a WiFi card into the SD card slot.
Alas all of the options above don't seem to lend themselves to allowing external audio into the camera.
The best option for doing external microphone input into a camera like the K-S1 (like the K-x, which also doesn't allow external microphones) is to record the audio outside of the camera with a external mic, and sync it with the video later in post-production. This also gives one the most flexibility in terms of mic vs camera placement too.
https://www.pentaxforums.com/forums/75-video-pentax-hdslrs/97504-pentax-k-x-e...recording.html Sync Sound: How to Work With Pocket Audio Recorders | Videomaker.com
etc
But if you felt really handy, I guess it wouldn't be impossible to remove the top of the camera and wire up a stereo microphone plug. But it may not be worth the trouble, since syncing external audio recorders isn't impossibly hard.