Coming back to the subject afresh I decided to re-read the instructions before looking at your update.
Page 10 states "The module consumes so few current that you can connect it through the included patch cable directly to the multichannel output of the receiver"
Page 11 - the picture clearly shows the patch cable between the receiver and 16ch 3972 connected to slot X2 A9 B9 C9 (left hand column of pins labelled FS_Impuls)
I think we agree on the above?
Do you have a multi meter?
I would suggest that you don't plug anything into the multi switch right now and try to follow my thoughts...
I will try to validate my suggestion this weekend with the kit I have
This (3972)is a switch. It is a single pole switch so can only switch one line either positive or negative but not both. We are told that it switches the negative/ground line
So this would mean for each channel we make only 2 connections to the switch for each channel (an in and an out for want of better terminology)
This would mean that we insert the switch into the negative/ground line only (see attached image)
Pic to follow shortly
I did not understand your post 100% but hopefully my post may add to the joint understanding
Update - see later post which over-rides some of this text