Could Tabby's star be beamed by a neutron star's jet causing irregular star spots?
I think this scenario is unlikely.  There is no evidence Tabby's star is near a neutron star.  Astronomers are monitoring Tabby's star very closely and there has not been any detection of the radio emission, gamma rays, or x-rays you would expect to see from a neutron star.  Also something as heavy as a nearby neutron star would have a lot of gravity probably show up in radial velocity measurements of the star.  Globs of dust, broken up comets, or more mundane stellar variability are a far more likely explanations for the weird dips seen in the star's light-curve.