How can I find other ways that I may be eligible for SGLI?
You may be able to get full-time SGLI coverage if one one of these descriptors apply to you:  if you are an active-duty service member; if you are a commissioned member of the National Oceanic and Atmospheric Administration NAOO or the US Public Health Service; if you are a cadet or midshipman of the US military academies; if you are a member, a cadet, or a midshipman of the ROTC engaged in authorized training and practice cruises; of you are a member of the Ready Reserve or National Guard assigned to a unit, and scheduled to perform at least 12 periods of inactive training per year;  if you are a volunteer in an Individual Ready Reserve IRR mobilization category; or if you are in nonpay status with the Ready Reserve or National Guard.
Are you saying that this covers the service person and military families are not eligible?
Service member that fall into the categories that have been described are eligible for SGLI.  It is specifically for servicemen.