[WPV]

This is offered only for information and has little practical value.
Within the BMW Repair Manual> K1300S>General Views/Templates>Wiring Harness>Functional Views and Overviews>Wiring Harness-View (Left or Right)
There is a pictorial view of the wiring harness installed on a naked cycle. It is of very little practical value, but may allow you to cross check some of the wire routing. Unfortunately the brains at BMW did not offer the capability to enlarge any part of the picture. The ambient air sensor appears, but you have to know where to look and what you are looking for. No mounting information is shown.

 

[WPV]

I have seen probes listed on ebay. Just make sure you get the ambient sensor not the intake sensor. Do you have cut wires where the socket for the sensor would be connected?

 

[WPV]

ebay>motors>motorcycle parts> search: "BMW K1300S ambient air sensor"> one listed. $7.00
eBay item number:275523162835
Check to see if this is what you need.