So according to an arcane section of the Student Union Constitution, (Article IX, section 8, clause 6),
There shall be no mid-term election for the positions of President or Vice-President except as provided for in Article III.
The relevant section (7) of Article III states,
If all positions of Union Executive Office mentioned in this Constitution shall become vacant, new Executive Elections shall be held.
So unless the President, Vice-President, Secretary, and Treasurer all get snuffed in one fell swoop, there is no new VP if the current one resigns mid-term.
And thus ends my hypothetical candidacy for Student Union Vice-President =). This means that Senate meetings will now be chaired by Andrew Brooks, and other VP responsibilities will shift around to the remaining E-boarders.