I’m interesting in adding lights to my two Billy bookshelves from IKEA without any drilling into the shelves since I may want to reverse it in the future. I want to light them via these 12v LED strips from Amazon: https://a.co/d/2GhrhK9
I am having a difficult time finding anything relating to the gauge/type of wire I should use. The wire is to connect the lights from shelf to shelf and I will be putting the lights in  45 degree diffusers similar to the image I’ve included.
For reference if you’re unfamiliar, Billy bookshelves are about 32 inches wide so the light strip piece on each shelf will be around 30 inches long and the wire length from shelf to shelf is about 12-15 inches. I am going to be using these solderless connecters to connect the wires to and from each light strip: https://a.co/d/aV7MOSU
My shelves each have 6 shelves, therefore there will be a total of 12 light strips all around 30 inches in length all connected by 2 12-15 inch pieces of wire between each light strip. In the photo I’ve included I attempted to give a visual of what the circuit will look like, the red parts signifying wire and blue parts signifying lights. What wire gauge would you recommend for this? Also, do you see any issues will my plan for lighting? I’ll include the other components I was going to use just to give you a better idea of my plans.

https://a.co/d/8RrlV94
https://a.co/d/0m69zYw
https://a.co/d/eHYYsxJ

I genuinely appreciate anyone’s help as I am really looking forward to making this work!! Thank you for taking the time!

What gauge wire to use lighting a series of LED strips?