The braking indices of pulsars may contain important information about the internal physics of neutron stars (NSs), such as neutron superfluidity and internal magnetic fields. As a subsequent paper of Cheng et al., we perform the same analysis as that done in the previous paper to other young pulsars with a steady braking index, n. Combining the timing data of these pulsars with the theory of magnetic field decay, and using their measured magnetic tilt angles, we can set constraints on the number of precession cycles, ξ, which represents the interactions between superfluid neutrons and other particles in the NS interior. For the pulsars considered in this paper, the results show that ξ is within the range of a few ×103 to a few ×106. Interestingly, for the Crab and Vela pulsars, the constraints on ξ obtained with our method are generally consistent with that derived from modeling of the glitch rise behaviors of the two pulsars. Furthermore, we find that the internal magnetic fields of pulsar with n < 3 may be dominated by the toroidal components. Our results may not only help to understand the interactions between the superfluid neutrons and other particles in the interior of NSs but also be important for the study of continuous gravitational waves from pulsars.