Note Mars opposing the Sun/Pluto conjunction. It has been my experience with electional charts that the Ascendant or Midheaven of the election aspects one or more planets in the native's chart with a conjunction or opposition within a few degrees. The Midheaven of the inauguration chart is 26 Capricorn and this opposes Donald Trump's Venus at 25 Cancer. The Ascendant of the inauguration chart at 14 Taurus does not make a connection to Trump's natal chart.  With J.D. Vance, the 14 Taurus inauguration Ascendant is opposition his Saturn at 10 Scorpio. Vance has no connection to the inauguration Midheaven. Regarding Elon Musk, there is no connection to either the Ascendant or Midheaven of the inauguration chart. This might indicate that Musk is not involved in the Presidency as time goes on.