[en] The gamma-ray burst (GRB) central engine intrinsic activity time $T_{\mathrm{c}\mathrm{e}}$ is usually described through either the γ-ray duration T₉₀ or through a generalized burst duration $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}$ that includes both the γ-ray emission and (when present) an extended flaring X-ray plateau. Here, we define a more specific operational description of $T_{\mathrm{c}\mathrm{e}}$, and within the framework of the internal–external shock model, we develop a numerical code to study the relationship between T₉₀ and $T_{\mathrm{c}\mathrm{e}}$, as well as between $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}$ and $T_{\mathrm{c}\mathrm{e}}$, for different initial conditions. We find that when $T_{\mathrm{c}\mathrm{e}}\lesssim <!--\; ???\; -->{10}^4$ s, late internal collisions or refreshed external collisions result in values of $T_{90}$ and $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}$ larger than $T_{\mathrm{c}\mathrm{e}}$, usually by factors of 2–3. For $T_{\mathrm{c}\mathrm{e}}\gtrsim <!--\; ???\; -->{10}^4$ s, the $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}$ is always a good estimator for $T_{\mathrm{c}\mathrm{e}}$, while T₉₀ can underpredict $T_{\mathrm{c}\mathrm{e}}$ when the late central engine activity is moderate. We find a clear bimodal distribution for $T_{\mathrm{c}\mathrm{e}}$, based on our simulations as well as on the observational data for T₉₀ and $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}$. We suggest that $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}$ is a reliable measure for defining “ultra-long” GRBs. Bursts with T₉₀ of order 10³ s need not belong to a special population, while bursts with $t_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{t}}><!--\; >\; -->{10}^4$ s, where the late central engine activity is more moderate and shows up in X-rays, may represent a new population. These conclusions are insensitive to the initial conditions assumed in the models.