Spatiotemporal techniques for signal coordination with actively transmitting extraterrestrial civilizations, without the need for prior communication, can constrain technosignature searches to a significantly smaller coordinate space. With the variable star catalog from Gaia Data Release 3, we explore two related signaling strategies: the SETI Ellipsoid, and that proposed by Seto, which are both based on the synchronization of transmissions with a conspicuous astrophysical event. This data set contains more than 10 million variable star candidates with light curves from the first three years of Gaia's operational phase, between 2014 and 2017. Using four different historical supernovae as source events, we find that less than 0.01% of stars in the sample have crossing times, the times at which we would expect to receive synchronized signals on Earth, within the date range of available Gaia observations. For these stars, we present a framework for technosignature analysis that searches for modulations in the variability parameters by splitting the stellar light curve at the crossing time.