  A recent time-integrated analysis of a catalog of 110 candidate neutrino
sources revealed a cumulative neutrino excess in the data collected by IceCube
between April 6, 2008 and July 10, 2018. This excess, inconsistent with the
background hypothesis in the Northern hemisphere at the $3.3~\sigma$ level, is
associated with four sources: NGC 1068, TXS 0506+056, PKS 1424+240 and GB6
J1542+6129. This letter presents two time-dependent neutrino emission searches
on the same data sample and catalog: a point-source search that looks for the
most significant time-dependent source of the catalog by combining space,
energy and time information of the events, and a population test based on
binomial statistics that looks for a cumulative time-dependent neutrino excess
from a subset of sources. Compared to previous time-dependent searches, these
analyses enable a feature to possibly find multiple flares from a single
direction with an unbinned maximum-likelihood method. M87 is found to be the
most significant time-dependent source of this catalog at the level of
$1.7~\sigma$ post-trial, and TXS 0506+056 is the only source for which two
flares are reconstructed. The binomial test reports a cumulative time-dependent
neutrino excess in the Northern hemisphere at the level of $3.0~\sigma$
associated with four sources: M87, TXS 0506+056, GB6 J1542+6129 and NGC 1068.
