  We upgrade the results of Borot--Bouchard--Chidambaram--Creutzig to show that
the Gaiotto vector in $\mathcal{N} = 2$ pure supersymmetric gauge theory admits
an analytic continuation with respect to the energy scale (which can therefore
be taken to be finite, instead of infinitesimal), and is computed by
topological recursion on the (ramified) UV or Gaiotto spectral curve. This has
a number of interesting consequences for the Gaiotto vector: relations to
intersection theory on $\overline{\mathcal{M}}_{g,n}$ in at least two different
ways, Hurwitz numbers, quantum curves, and (almost complete) description of the
correlators as analytic functions of $\hbar$ (instead of formal series). The
same method is used to establish analogous results for the more general
Whittaker vector constructed in the recent work of Chidambaram--Dolega--Osuga.
