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@misanderousmisfit this was going to be super long and also I have a picture, so I decided just to make a post.
Okay, SO.
I just posted this gif with a new set, prompting @misanderousmisfit to say, "Wait how did I not notice that Mav takes his own wings and snaps them on the casket??!!!"
Then she asked for an explanation, and I am happy to provide one, not least of which because I actually already researched this and explained it to someone else like right after TGM came out.
What Maverick does with his wings at Ice's funeral is based on a tradition by the SEALs. Similar to naval aviators, Navy SEALs are given a specific pin that is unique to their role. Pilots have wings; the SEALs have what is called a Trident. It's a symbol not only of the group they belong to, but of all the work they had to do to acquire this specification.
When a SEAL team loses a member, the other members hammer their Tridents into the top of the casket. It's basically taking an incredibly valuable item and giving it to your friend as a sign of respect, and to show that a piece of you is going with him.
The reason they punch them into the casket like that is just to drive the metal into the wood, so the pins stay there.
Those are Maverick's wings. He is giving them to Ice to send a piece of him with him.