So, the rule is that if you have a single character speaking across multiple paragraphs, you don’t use end quotes on those paragraphs. I get the intent of the rule, but I think it looks awful and is jarring.
What I have been doing for a long time, is to insert a minor action at the end of that paragraph or the start of the next. I don’t even notice that I am doing it anymore, it just feels natural to have a character gesture or emote in some way every so often.
The only reason that this came to mind is that one of my new readers pointed out a spot in Chapter 50 where I had used end quotes on a paragraph break of continuous speech. I edited in a minor action instead, the character was recalling a previous thought process, so I had him lean back in his chair and look up, which is the sort of thing people often do during that sort of thought.
One of the advantages of publishing a serial online, you potentially get some good feedback. :)
I’d say it depends on the length of the dialogue. If we’re talking about 2-3 lines, then yeah, it should only be done on switching. If we’re talking about a speech that lasts several pages, I would think that it should be clear from context clues who is speaking.
Anyway, don’t get hung up on rules! Write how you want! Have a style!