Can a "former" brother-in-law (i.e. the divorce having occurred two years ago) NOT living with a taxpayer be claimed for dependency exemption (as a qualifying relative) assuming that the support test, gross income test, joint return test, and citizenship or residency tests have been met? In other words, does a "former" brother-in-law get the same treatment as a "current" brother-in-law in terms of not needing to live with the taxpayer for a full year, or would he be treated as a member of the household (i.e. an unrelated party) ONLY if he were to actually live with the taxpayer for a full year?

Former brother-in-law is not your relative.

Agreed; to be claimed, the former brother-in-law MUST be a member of your household.