How to tell a pulsar is rotation-powered or accretion-powered? We need to calculate P/Pdot?

A pulsar may switch between theses two states.

For a rotation powered pulsar, it can pulse and, the pulsed Lx can be much larger than the luminosity given by its rotation?  

If Lx is very small, smaller than the luminosity given by its rotation, how to tell it is rotation-powered or accretion-powered? There are not necessarily X-ray pulsations

You can see I am asking a very tricky scenario.
The spin behaviour of the two types of pulsar would usually be quite different. The $\dot{P}$ for a rotationally powered pulsar is always positive, and higher order time derivatives of $P$ are quite small. This is because the rotational kinetic energy is powering the pulsar emission and the neutron star continually spins down as it loses rotational energy.

Accretion powered pulsars can have very variable spin down or spin up characteristics, because they are powered by mass transfer and accretion in binary systems, and are influenced by a variety of factors affecting the accretion flow and how it couples to the pulsar magnetic field. The rates of spin down can be much higher than can be plausibly be accounted for by magnetic spin down as in a rotationally powered pulsar. Spin up cannot be accounted for in a rotationally powered model and neither can sign reversals or dramatic variability in $\dot{P}$.

Additionally, an accretion-powered pulsar would necessarily need to be in a short period binary system - therefore there would be a very obvious periodic modulation in the pulse period caused by the doppler shift as it travels in ts orbit.