Thank you for posting!
The cause of the problem is the type of video cable you are using to connect non-working display to the UD-6950Z dock. The cable is not compatible, which is why the display is not working.
To expand further, only DisplayPort to DisplayPort video cables (cables with a DisplayPort connector on both ends) or HDMI to HDMI video cables (cables with a HDMI connector on both ends) can be used to connect external monitors to the dock.
In almost all cases, a cable with a USB-C connector on one end of the cable and a DisplayPort connector on the opposite end of the cable can only work in one ‘direction’ from a USB-C source to a DisplayPort destination. They will not work in the opposite direction as you are attempting.
I say ‘almost all cases’ because in our experience helping others we have been made aware of this Moshi USB-C to DisplayPort cable → https://www.moshi.com/en/product/usb-c-to-displayport-cable-5-ft-1-5-m/white?ref=category:43 that purports to work in both ‘directions’.
In our experience helping others, we have found that these ‘bi-directional’ cables are not compatible with any of our Plugable products.
An alternative solution would be to connect the non-working display to the dock using the aforementioned DisplayPort to DisplayPort or HDMI to HDMI video cable. If the display does not have a DisplayPort or HDMI video input, then I am afraid we do not have any solutions to offer.
Apologies that we could not be of more help in this specific case, and thank you in advance for your understanding!