Turn Signal Multiswitch Replacement on a 2013 Sport

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Mazda CX5
Hi, I need help installing a replacement turn signal multiswitch. My wife's 2013 Mazda CX-5 Sport has been suffering from flickering headlights whenever she uses the turn signal. It doesn't matter which way you turn switch, left or right the headlights flicker. So after some research, I assumed that I needed to replace the turn signal multiswitch. I'm very handy with tools and car electronic installs, so I figured that I could tackle this replacement.

Unfortunately, I ran into an issue where I pulled apart the steering column to install the new multiswitch, but the OEM multiswitch is hardwired into the car. Sorry for not posting pics, but the there's wires running into the multiswitch that can't be disconnected. Additionally, the replacement has the wires intact and seems like you could just pop it in. What am I missing? Should I cut and solder the wires from the car to the new multiswitch?

I appreciate all of you help.
 
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