The sensors would detect if from the source the parabolic is single or multiple parabolic .
That alone rules out quasar or pulsar natural phenomina. The problem is they may have developed a single parabolic with tube bundle perimeter. The AC ionic wave tube bundle as a thruster is not detectable across interstellar distances for being corona as such less luminous. Nonetheless such a pulse rocket if detectable is in our back yard only a few light years away or less. Unless their space ship has the colossal dimensions of the Star Wars Death Star.
If the alien pulse nozzle blasts at laser disentigration the sensitive instrumentation should look for Doppler blue shift because pointed in our direction the ship is decelerating. If the ship is accelerating away then red shift but unlike pulsar or quasar the fingerprint comparison with a real quasar or pulsar is different if of artificial origin.
The laser pulse motor used by aliens that is something that should interest SETI. If some spaceship in interstellar space is using laser pulse close enough to our Solar System with the nozzle pointed in our direction, it would be detectable by sensitive instrumentation and differ from a pulsar or quasar. How? For one thing mobility. Another is an abrupt stop in signal where they shut off their motors or do a change in direction. Most likely for Interstellar travel the pulses are nuclear fusion pulses but not excluding iceball disentigration pulses.