What exactly is "the rotating lighthouse model" in the context of a double pulsar? The introduction to Testing the rotating lighthouse model with the double pulsar system PSR J0737-3039A/B (open access) says:

The double pulsar system PSR J0737-3039A/B was discovered by Burgay et al. (2003) and Lyne et al. (2004). This system consists of a 22-ms pulsar (hereafter A) and a 2.8-s pulsar (hereafter B) with an orbital period of 2.4 h. This discovery has provided a laboratory for the study of relativistic gravity and gravitational radiation (Kramer &amp; Wex 2009). The system has several strange features that challenge the current understanding of pulsars and provide an uncommon opportunity to improve pulsar theories. One of the most interesting properties is the observed modulation of each pulsar's signal by the energy flux from the other, as evidenced by each pulsar's modulation period being approximately equal to the other pulsar's pulse period (McLaughlin et al. 2004a,b). Freire et al. (2009b) proposed a technique for analysing the arrival times of the pulsars’ pulses and their mutual modulations which could yield the sense of rotation of each pulsar with respect to its orbital motion, among other quantities.** In this paper, a complementary technique is presented with the same objective, but using measured periods rather than arrival times. The principal benefit of our approach is that it is simpler and more intuitive. If the validity of either of these techniques is confirmed, not only will new insights be gained but also the correctness of the lighthouse model will be empirically assessed beyond dispute.

I think there is a lot going on here, more than I can take in all at once. So I'd like to simply ask:
Question: What exactly is &quot;the rotating lighthouse model&quot; in the context of a double pulsar? Modulation is mentioned in this and the other papers, and an interaction with each others' magnetospheres is suggested to explain it, but is that part of &quot;the rotating lighthouse model&quot;?
It seems that the authors are just referring to the accepted model of a pulsar, i.e. a neutron star spinning and emitting beams of radiation at its poles. In that sense, the term is used here no differently than it would be in the context of an isolated pulsar. It's just a very simple way of visualizing why an observer far away appears to see periodic pulses rather than constant emission.
If the lighthouse model is correct, then the beams from one pulsar may interact with the other pulsar, which in turn would cause changes in the second pulsar's emission each time the beam sweeps across it. The modulation period would then be approximately equal to the rotational period of the second pulsar - not precisely, though, because of orbital motion; hence, the comparison between Earth's sidereal day and solar dat.
Modulation of pulse strength and features therefore isn't a feature of the lighthouse model but rather a consequence of it, present in some binary pulsar systems but of course not in isolated pulsar emission.