The way this reads, it seems like the seat will be left vacant
and filled by the runner-up. To me, those are mutually exclusive things.
Maybe something like: Should a Secretary or Core Committee position become vacant with less than 4 months remaining in its term, the Secretaries and Core Committee may (at their discretion) invite the runner-up in the most recent election to fill the seat until the next scheduled election. (The runner-up is the person with the second-highest vote totals in elections for secretary and with the fifth-highest vote totals in elections for Core Committee.)
If two or more Secretary positions become vacant at the same time, a special election must be called immediately for all seats.
-- J.T.