We investigate the statistics of photons emitted by tunneling electrons in a single electronic level plasmonic nanojunction. We compute the waiting-time distribution of successive emitted photons $w(tau)$. When the cavity damping rate $kappa$ is larger than the electronic tunneling rate $Gamma$, we show that in the photon-antibunching regime, $w(tau)$ indicates that the average delay-time between two successive photon emission events is given by $1/Gamma$. This is in contrast with the usually considered second-order correlation function of emitted photons, $g^{(2)}(tau)$, which displays the single time scale $1/kappa$. Our analysis shows a relevant example for which $w(tau)$ gives independent information on the photon-emission statistics with respect to $g^{(2)}(tau)$, leading to a physical insight on the problem. We discuss how this information can be extracted from experiments even in presence of a non-perfect photon detection yield.
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