I wanted to plug in a headset to take calls on the P1 and noticed that while it was playing audio into the headset, it was still picking up audio from the built in mic.
Looking at the sound settings showed only the “Digital Jack” visible. None of the solutions previously posted (from forum posts throughout 2011-2014) no longer worked.
The solution that DID work for me was uninstalling the device in Device Manager, including all drivers and then downloading them again from the Lenovo Support Page here: https://pcsupport.lenovo.com/se/en/products/laptops-and-netbooks/thinkpad-p-series-laptops/thinkpad-p1-type-20md-20me/downloads
After reinstalling, and plugging in my headset, I could now see the Rear Panel 3.5mm jack in sound properties.