  Line-intensity mapping (IM) experiments seek to perform statistical
measurements of large-scale structure with spectral lines such as 21cm, CO, and
Lyman-$\alpha$ (Ly$\alpha$). A challenge in these observations is to ensure
that astrophysical foregrounds, such as galactic synchrotron emission in 21cm
measurements, are properly removed. One method that has the potential to reduce
foreground contamination is to cross correlate with a galaxy survey that
overlaps with the IM volume. However, telescopes sensitive to high-redshift
galaxies typically have small field of views (FOVs) compared to IM surveys.
Thus, a galaxy survey for cross correlation would necessarily consist of pencil
beams which sparsely fill the IM volume. In this paper, we develop the
formalism to forecast the sensitivity of cross correlations between IM
experiments and pencil-beam galaxy surveys. We find that a random distribution
of pencil beams leads to very similar overall sensitivity as a lattice spaced
across the IM survey and derive a simple formula for random configurations that
agrees with the Fisher matrix formalism. We explore examples of combining
high-redshift James Webb Space Telescope (JWST) observations with both a
SPHEREx-like Ly$\alpha$ IM survey and a 21cm experiment based on the Hydrogen
Epoch of Reionization Array (HERA). We find that the JWST-SPHEREx case is
promising, leading to a total signal-to-noise of ${\sim}5$ after 100 total
hours of JWST (at $z=7$). We find that HERA is not well-suited for this
approach owing to its drift-scan strategy, but that a similar experiment that
can integrate down on one field could be.
