You shouldn’t labor to make connections where there are none. Some candidates have largely unrelated ideas and methodologies. It is not particularly important to connect all of your teaching interests to writing interests. You might happen to be law and literature scholar who is willing to teach tax. Schools will view this as a good thing.
While not all schools will require academic candidates to submit a written scholarly agenda, you should spend time clarifying your agenda and be prepared to discuss it in some detail (few schools will require clinical candidates to submit a written scholarly agenda). The research agenda is meant to assure law school hiring committees that you are a person who can generate interesting ideas that will sustain a productive scholarly career. Its purpose is not to bind you to a particular course of research; some professors adhere to the agenda they proposed while on the market, while the scholarly agenda of many others evolves as they become interested in new avenues of inquiry. As with your job talk paper, you should have several different “pitches” of your agenda prepared—for example, you might prepare a one sentence, one paragraph, and one page version of your research agenda.A statement of the candidate’s scholarly agenda has no set form; typically the statement is one to two pages in length. Ideally, the agenda should contain a clear narrative of your developing scholarly interests. You might begin by identifying the context in which your interests were sparked—perhaps one of your law school classes, your SAW or Substantial, your undergraduate or joint degree, or your practice experience. Then, describe how your job talk paper manifests these interests. Include the thesis of the paper, its stakes, and the way in which it relates to your overall agenda. At a minimum, you should be able to describe the tentative claims of one or two papers you have in progress or that you would like to write in the future and how they will contribute to the agenda you have laid out. Some candidates choose not to circulate a scholarly agenda and instead rely on circulating a CV with annotated descriptions of their publications. If you choose this route, it is important that you include annotated descriptions of works in progress that you plan to write. It is not necessary that a work-in-progress be circulable in order for it to be included on your CV, but it is necessary that you can write a cogent and interesting description of its central claims.