= Solution
For a $t\to cZ$ search, the cleanest neutral-boson reconstruction is $Z\to e^+e^-$ or $\mu^+\mu^-$: require an <Lepton isolation>[isolated] opposite-sign same-flavour pair near the $Z$ <mass> and a <jet> forming the top <mass> with that pair. In top-pair events, tagging the other top through its ordinary $bW$ decay provides a <Bottom-quark jet tagging>[bottom jet] and, if its $W$ is leptonic, another <Lepton isolation>[isolated] lepton and <missing transverse momentum>. Kinematic reconstruction and heavy-flavour information help reject vector-boson-plus-jets and other backgrounds. Hadronic or invisible $Z$ decays have higher rate but less distinctive backgrounds or incomplete <mass> reconstruction.
For the literal $t\to cZ\gamma$ channel, additionally require a prompt <particle isolation>[isolated] <photon> and reconstruct the top with $Z+\gamma+$<jet>. For the alternative $t\to c\gamma$, use an <Particle isolation>[isolated] energetic <photon> and <jet> near the top <mass>, again exploiting the other top as a tag. These are search signatures; no present-day observation claim is needed to interpret the historical question.
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