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For Discussion: The language of 871 U.S. Code.

My reading is that it requires both a threat (as distinguished from an advocacy), and that the successor actually be the next in line.

Section 871. Threats against President and successors to the Presidency

(a) Whoever knowingly and willfully deposits for conveyance in the mail or for a delivery from any post office or by any letter carrier any letter, paper, writing, print, missive, or document containing any threat to take the life of, to kidnap, or to inflict bodily harm upon the President of the United States, the President-elect, the Vice President or other officer next in the order of succession to the office of President of the United States, or the Vice President-elect, or knowingly and willfully otherwise makes any such threat against the President, President-elect, Vice President or other officer next in the order of succession to the office of President, or Vice President-elect, shall be fined under this title or imprisoned not more than five years, or both.
(b) The terms ''President-elect'' and ''Vice President-elect'' as used in this section shall mean such persons as are the apparent successful candidates for the offices of President and Vice President, respectively, as ascertained from the results of the general elections held to determine the electors of President and Vice President in accordance with title 3, United States Code, sections 1 and 2. The phrase ''other officer next in the order of
succession to the office of President'' as used in this section shall mean the person next in the order of succession to act as President in accordance with title 3, United States Code, sections 19 and 20.

The other relevant section 18 USC 115. The defense department is one of those listed in 5 USC 101.

Section 115. Influencing, impeding, or retaliating against a Federal official by threatening or injuring a family member

(a)(1) Whoever -
(A) assaults, kidnaps, or murders, or attempts or conspires to kidnap or murder, or threatens to assault, kidnap or murder a member of the immediate family of a United States official, a United States judge, a Federal law enforcement officer, or an official whose killing would be a crime under section 1114 of this title; or
(B) threatens to assault, kidnap, or murder, a United States official, a United States judge, a Federal law enforcement officer, or an official whose killing would be a crime under such section, with intent to impede, intimidate, or interfere with such official, judge, or law enforcement officer while engaged in the performance of official duties, or with intent to retaliate against such official, judge, or law enforcement officer on account of the performance of official duties, shall be punished as provided in subsection (b).
(2) Whoever assaults, kidnaps, or murders, or attempts or conspires to kidnap or murder, or threatens to assault, kidnap, or murder, any person who formerly served as a person designated in paragraph (1), or a member of the immediate family of any person who formerly served as a person designated in paragraph (1), with intent to retaliate against such person on account of the performance of official duties during the term of service of such person, shall be punished as provided in subsection (b).
(b)(1) An assault in violation of this section shall be punished as provided in section 111 of this title.
(2) A kidnapping, attempted kidnapping, or conspiracy to kidnap in violation of this section shall be punished as provided in section 1201 of this title for the kidnapping, attempted kidnapping, or conspiracy to kidnap of a person described in section 1201(a)(5) of this title.
(3) A murder, attempted murder, or conspiracy to murder in violation of this section shall be punished as provided in sections 1111, 1113, and 1117 of this title.
(4) A threat made in violation of this section shall be punished by a fine under this title or imprisonment for a term of not more than five years, or both, except that imprisonment for a threatened assault shall not exceed three years.
(c) As used in this section, the term -
(1) ''Federal law enforcement officer'' means any officer, agent, or employee of the United States authorized by law or by a Government agency to engage in or supervise the prevention, detection, investigation, or prosecution of any violation of Federal criminal law;
(2) ''immediate family member'' of an individual means - (A) his spouse, parent, brother or sister, child or person to whom he stands in loco parentis; or
(B) any other person living in his household and related to him by blood or marriage;
(3) ''United States judge'' means any judicial officer of the United States, and includes a justice of the Supreme Court and a United States magistrate judge; and
(4) ''United States official'' means the President,
President-elect, Vice President, Vice President-elect, a Member of Congress, a member-elect of Congress, a member of the executive branch who is the head of a department listed in 5 U.S.C. 101, or the Director of the Central Intelligence Agency.
(d) This section shall not interfere with the investigative authority of the United States Secret Service, as provided under sections 3056, 871, and 879 of this title.