If "immersion" is your goal, just never use the map at all.

I'd be happy with just the option to remove the annoying flashing quest pins if you go from the journal to the map. But if there is an option I haven't seen it. (I know I can turn the quest markers off entirely, but sometimes I want them there, I just don't want one flashing constantly whenever I open the map.)

I know it's just the latest in a long list of examples which imply ZOS thinks anyone wanting to do quests is very stupid and incapable of finding anything which isn't blindingly obvious, so we have to have important quests which cannot ever be removed from the journal just in case you're not sure where to pick it up again, quest givers following you constantly until you accept, markers on absolutely everything which might possibly be relevant, especially if you're asking to put any effort into looking for it and "puzzles" which consist of clicking 3 things in the correct order after a book, an NPC and the quest journal have all told you what that is.

But for whatever reason this is the one which really gets on my nerves. Possibly because I just don't like repetitive flashing animations in general. Yes I often want to look up a quest in the journal, then look at the map to see where to go, but I am capable of understand that the quest marker is showing me the location without it going "it's here, it's here, it's here, it's here, it's here" and making it difficult to see anything in the surrounding area because it's covered by the effects.