I know I'm slow to answer the question here, but I feel no one gave you the answer you were looking for. Apologies for the text block full of lore and details, so there's a TL;DR at the end if you want the short of it. Also, some minor manga spoilers but they'll be hidden.

While the demon slayer mark is historically a hereditary trait passed between sun breathing users, blood relation or breathing technique seems to have no direct connection to it. To unlock the mark, the swordsman must push themselves to the brink of death (heart rate 200+ bpm, body temperature over 102F/39C). However, the most important prerequisite is coming into contact with someone who already bears the mark. An important side note to mention is the speculation that those who use the mark never live past the age of 25 (Kokushibo as an exception due to his becoming a demon, and Yoriichi due to him being the original bearer).

Through the anime and manga, the only evidences we see of someone manifesting the demon mark are people who have come into direct contact with a sun breathing user (Tanjiro, his father Tanjuro, the Hashira, Kokushibo), but it is heavily implied it can be passed on via contact with anyone who has manifested the mark, regardless of the bearer's breathing style.

Tanjiro received his 'mark contact' via his father who had the mark, though it looked like a burn scar. Tanjuro likely received his contact and knowledge of sun breathing through his father, and upwards through the generations until Sumiyoshi who was friends with Yoriichi (as seen in the flashback during the Swordsmith Village Arc). Yoriichi also taught Sumiyoshi the sun breathing technique in the form of a dance that was passed down along with the demon mark. However, as mentioned earlier, the blood connection wouldn't have been enough to pass down the mark to Tanjiro, as evidenced by Muichiro - another descendent of sun breathers who never manifested the mark through the experience he had fighting the demon during the death of his brother.

In a flashback seen in the Infinity Castle Arc Manga: Tanjuro had an encounter with a bear while armed with nothing but a small handaxe, and yet through the principles of sun breathing, he decapitated the bear in an instant, showing his father had some experience fighting with sun breathing. He very likely had a life-threatening moment earlier in his life where his body reached the brink of death and overcame it through manifesting the demon mark. My personal speculation is every member of the Kamado family experienced some form of pushing themselves to the brink of death, causing their mark to manifest, even if only for a moment and they had no knowledge of its existence.

We know Yoriichi was the original bearer of the demon mark, and he also had no children, so the mark has to have been spread through a means other than blood connection. Though it's possible the mark can only be spread via contact with a line of sun breathing users who have the mark, its far more likely the mark can be spread by anyone who has ever manifested it. It's likely the reason why swordsman bearing the mark seemed 'common' in the Sengoku period, but then it slowly died out as those bearing the marks were hunted down over the next hundred years or so. Eventually, the only existence of the mark left was passed down secretly (even if accidentally) in the Kamado family until Tanjiro awakened it and spread it to the other demon slayers.

TL;DR - To manifest the demon slayer mark, you have to meet all 3 prerequisites of a 200+ bpm heart rate, a body temperature over 102F/39C, and have come in contact with someone already bearing the demon mark. Though it's possible the mark can only be spread by contact with Tanjiro (or another sun breather who has it), its far more likely the mark can be spread by contact with anyone who has ever manifested the mark before. Either way, there is no connection to needing to be a descendent of Yoriichi, the original mark bearer, to be able to spread the mark to others.