Hi Ryan,
I suspect something else happened, because even if for example, your Panigale V4 has a Normally Open switch from the factory but your RCS17 came with a Normally Close switch,
it only means the light turns on backward, so the light is on when the level is not pressed and turns off when the light is pressed.
So let's do these steps:
First, check whether your light bulb is good or bad, by plugging back the stock switch from the stock master cylinder.
If after plugging back the stock switch, your light bulb is still not on, that means you need to replace your light bulb.
But if the light bulb is on after plugging back the stock switch, then either the switch in your RCS17 is bad or maybe the new wiring is bad.
When I install my RCS17 Corsa Corta or RCS19 Corsa Corta, I peel off the switch that came with the RCS 17/19 Corsa Corta and then plug in the switch that came from my original Brake Master Cylinder.
The stock switch from your stock master cylinder should plug into the RCS (at least for my RCS Corsa Corta model). This way, you don't have to do any splicing of factory wire or replace socket.
Please also try this, and I hope your 17 RCS (I believe your RCS is a NON-Corsa Corta model can accommodate a stock switch like the RCS Corsa Corta model).
Last, for your reference, there are 2 kinds of switches. The Normally Open and Normally Closed.
Below is an image showing a Normally Closed Switch that I believe comes with your RCS17 kit.
