On 2 machines (Dell Latitude 7480) already, I'm facing the same issue. The type-c port doesn't seem to recognize when a docking station is plugged in. When I plug in the WD15, the light on the connector doesn't light up. On both laptops, the issue occurred after a standard start of Windows.
I thought it's a hardware issue, so I got the first laptop and made a reset for Windows 10 in order to send it for RMA. For my surprise, everything worked after that.
So apparently it's a software problem. I need assistance fixing the 2nd one without OS reset. I can send both service tags if necessary.
All latest updates were installed from Dell Command Update.
Does the dock otherwise work, i.e. your only concern is that light? For what it's worth, I have a WD15 and when I connect an XPS 13, even one that's completely powered off, the dock cable light comes on -- so it's probably at most a firmware issue rather than software given that there's no software to handle that light when it's powered off. However, when my wife plugs her ThinkPad T480 into the dock, the light never comes on even though the dock works perfectly with that system, including charging it even when it's off. If it really bugs you, have you installed the latest firmware for both the dock and the system? The former in particular might not come up in Dell Command Update, so try going to support.dell.com and browsing the product catalog for the dock itself.