Regarding Domelight Wiring

[ladybugblazer]

So I decided to start digging and finding out why my dome light wasn't working today. I took off the cover and found found that both the leads were hanging only with a few strands of wire and bundles of electric tape. After taking off the electric tape to see what was under I was greeted with the attached image. Not sure why there are 3 wires I labelled them 1, 2, and 3 in the picture. Two are yellow (1 & 2) and one is red (3). The two that are yellow (1 & 2) seem to be going to the back of the truck, and the one that is red (3) seems to be coming from under the headliner towards the front of the truck. Wires 2 & 3 get combined on one of the leads. Could it be possibly that this is to continue power to the back lights?

My plan was to cut off the two bad leads and crimp/heat shrink in two new ones that I already bought, but because there are three wires I need to figure out how to connect those 3. I don't wanna solder. I found this WAGO Connector of amazon and was thinking about using this:
https://www.amazon.com/Wago-221-413-...dp/B06XGYXVXR/
But I was just wondering if this is a good fix or if I am even doing this job right