In OP episodes there is a small transition/break mid-episode that shows one of the main characters picking up their most recognized item/weapon (prior it was a hat floating away or something or there were two of these). I used to think this was done using the character who appears in the main scene(s) for that episode but I just chanced across a few that had had Brooke picking up his violin and Chopper his backpack and no appearance of them. So I ask is it completely random or does it relate at time?
On One Piece Wiki there is this page about the Eyecatchers, which seems to confirm your guess:
In One Piece, there are two eyecatchers in every episode, and each one shows one of the Straw Hat Pirates, usually the ones who had the most significance in the episode, accompanied by a short excerpt of their respective themes.
Moreover there are a lot informations, as the number of appearance of each character in the transitions and some trivia about the criteria behind the choice of the character, e.g.
The characters of One Piece get a personal eyecatcher only after they join the Straw Hat Pirates. For example, Brook, despite fighting alongside the Straw Hats for the entirety of the Thriller Bark Arc, had no eyecatcher until his official recruitment. Sanji is the exception, having an eyecatcher just two episodes after his initial appearance, long before joining the crew.
In every anime I've seen with mid-episode transactions (MT) I've noticed five types of MTs.
- Fixed - The same MT since episode 1 untill the end (very rare);
- Changing by season - It changes depending on the season
- Changing by arc - It changes depending on the arc;;
- Changing by character reference - It focus on one or more characters of the anime (like One Piece);
- Mix of 2, 3 and/or 4 - It is what is is (LOL).
There isn't any source that comproves this at least I haven't found any.
However, as in One Piece or any other animes that use MTs 3, 4 and 5, the MT seems to focus on the "main character of that specific episode" or the "Location of the episode" (this happens a lot in Fairy Tail S2, just an example though).
One Piece follows the same pattern, and the MT focus on the main character.
However, other characters can't be "forgotten" therefore they appear in the respective MTs.
Once again, I haven't found any official source that confirms this it's just a pattern I have seen in several animes not only one piece. The fact that there isn't any official source might be a proof that it's not that important to be mentioned and it's just plain random.