I was thinking that pulsars inside nebulae should have a plerion (pulsar wind nebula), with the equatorial shock wave being the prominent feature (along with the astrophysical jet).
As for some related stuff; from certain angles, a pulsar would be distinguishable by the rapid twinkling from the astrophysical jet due to relativistic beaming. Another idea is for hotspots to appear on the magnetic poles of the neutron star where matter falls in from the accretion disk, along with rare but sudden starquakes that makes the pulsar extremely bright. In binary systems, if the companion star of a pulsar is close enough it will form a roche lobe causing the pulsar to turn into a microquasar.
https://heasarc.gsfc.nasa.gov/images/ob ... ate_cv.gif
http://iopscience.iop.org/1538-3881/141 ... aj374957f3
http://www.issibern.ch/teams/millisecpu ... /simul.jpg
https://upload.wikimedia.org/wikipedia/ ... -sheet.gif
Sorry if I seem demanding, I am bad with wording
(EDIT: Edited too many times to count)