  We revisit the model of an AdS$_2$ black hole in JT gravity evaporating into
an external bath. We study when, and how much, information about the black hole
interior can be accessed through different portions of the Hawking radiation
collected in the bath, and we obtain the corresponding full quantitative Page
curves. As a refinement of previous results, we describe the island phase
transition for a semi-infinite segment of radiation in the bath, establishing
access to the interior for times within the regime of applicability of the
model. For finite-size segments in the bath, one needs to include the purifier
of the black hole microscopic dual together with the radiation segment in order
to access the interior information. We identify four scenarios of the entropy
evolution in this case, including a possibility where the interior
reconstruction window is temporarily interrupted. Analyzing the phase structure
of the Page curve of a finite segment with length comparable to the Page time,
we demonstrate that it is very sensitive to changes of the parameters of the
model. We also discuss the evolution of the subregion complexity of the
radiation during the black hole evaporation.
