The 61-year-old Maywood resident is the second openly gay person ever to have been elected to the New Jersey legislature.
Eustace said he is moving on to a "different position" but did not disclose anything more, the article says.
Eustace and his late partner Kevin Williams were New Jersey's first openly gay couple to apply to the state for joint adoption in the 1980s. The couple later adopted three children who had contracted AIDS.
Eustace served as Maywood's mayor from 2008 to 2011 before he was elected to Assemblyman, representing North Jersey's 38th legislative district.
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