I found a service manual with schematic and BoM for the Kaoss Pad 3 here (I couldn't find an official link from Korg). 

The 50 pin ZIF connector on the motherboard (KLM-2735) is labeled CN1B.  Pins 3-12 are broken out on the right hand side. 

The schematic shows that pins 4 and 6 send the line in (signals LINE_L and LINE_R) to the panel board (KLM-2734).  The line in is processed by a volume control circuit and sent back to pins 8 and 10 of CN1B as VR_L and VR_R.  

At first I connected pins 4 and 6 directly to pins 8 and 10 and tested for audio passthrough.

It sounded pretty good for a fuzz pedal if I hit it hard enough with power chords, but something was clearly wrong.  A closer look at the block diagram shows the line in is stepped down from 10VA to 5VA before reaching the ADC.  We're probably saturating the second buffer by driving it directly from the line input. 

I built the volume control circuit on some stripboard, minus the switch for selecting mic input as I don't have that board.

Testing again I got clean audio passthrough with no effects applied.