  We present a search for continuous gravitational wave signals from an
unidentified pulsar potentially powering HESS~J1427-608, a spatially unresolved
TeV point source detected by the High Energy Stereoscopic System (HESS). The
search uses a semi-coherent algorithm, which combines the maximum likelihood
$\mathcal{F}$~statistic with a hidden Markov model to efficiently detect and
track quasi-monochromatic signals that wander randomly in frequency. It uses
data from the second observing run of the Advanced Laser Interferometer
Gravitational-Wave Observatory. Multi-wavelength observations of the HESS
source are combined with the proprieties of the population of TeV-bright pulsar
wind nebulae to constrain the search parameters. We find no evidence of
gravitational wave emission from this target. We set upper limits on the
characteristic wave strain $h_0^{95\%}$ (for circularly polarized signals) at
$95\%$ confidence level in sample sub-bands and interpolate it to estimate the
sensitivity in the full band. We find $h_0^{95\%} = 1.3\times 10^{-25}$ near
185~Hz. The implied constraints on the ellipticity and \textit{r}-mode
amplitude reach $\epsilon\leq 10^{-5}$ and $\alpha \leq 10^{-3}$ at 200~Hz,
respectively.
