It's not as difficult to find a thesis as many students think. It's a lot like finding any research project. See https://www.eecs.mit.edu/academics-admissions/undergraduate-programs/opp.... For one thing, an M.Eng. thesis supervisor need not be a Course VI faculty member. Students thinking about continuing directly into the Course VI Ph.D. program will find it strongly to their advantage to establish an early research relationship with EECS labs and faculty. However, any School of Engineering or Science faculty member (including the Media Lab) and most Department-affiliated senior research staff members may supervise an M.Eng. thesis. Use the Faculty and Advisor listing to look for supervisors. If you wish to be supervised by a faculty member outside the School of Engineering or Science, or by a staff member not listed in the Research Supervisor list, you may request permission. Consult Anne Hunter.
Find a project which is of direct and intense interest to you and which will give you a maximum opportunity not only to learn about the subject being investigated, but also about proper methods of technical investigation. If you are already a graduate student in the M.Eng. program, you will want to avoid projects so remote from your current training that acquiring the necessary background will cause excessive delay.