While I could point you to historical works about Yemen, the current conflict is unfortunately I think not so much grounded in that history as it is in the events of the past 20 years that under the rules of this subreddit are forbidden from discussion. I.e. I don't think pointing you to the history of, say, Egypt's intervention in Yemen in the 1960s will tell you very much about what is happening there now.

I would encourage you to instead look at overviews of the conflict as published by think tanks like the Brookings Institute, the Carnegie Endowment, and Crisis Group.

For example, this set of articles from Carnegie: https://carnegieendowment.org/sada/78832

I know I’m incredibly late here, but I would recommend that you read Yemen in Crisis: Road to War by Helen Lackner. It gives a detailed view of the factors that lead to the current civil war, as well as the reality of the US involvement in it.