I'm not familiar with the adapter you have. However, I did a side-by-side comparison for both. From what I'm seeing in the wiring schematics, they look basically the same.
If you look below, the first 4 pics are for the 5.3 and the last 4 are for the 6.0. Take a look through them and use them as a reference. Note: I had to cut each page in half to make them readable for you. I did overlap each so you can follow from one to the next.
Let me know if this helps or if you have other questions.
See pics below.
Images (Click to enlarge)
Friday, May 13th, 2022 AT 9:13 PM