The outer halo globular cluster NGC 6229 has a peculiar horizontal-branch (HB) morphology, with clear indications of a bimodal HB and a "" gap ÏÏ on the blue HB. In this paper, we present extensive synthetic HB simulations to determine whether peculiar distributions in the underlying physical parameters are needed to explain the observed HB morphology. We Ðnd that a unimodal mass distribution along the HB can satisfactorily account for the observed HB bimodality, provided the mass dispersion is substantially larger than usually inferred for the Galactic globular clusters. In this case, NGC 6229 should have a well-populated, extended blue tail. A truly bimodal distribution in HB masses can also satisfactorily account for the observed HB morphology, although in this case the existence of an extended blue tail is not necessarily implied. The other two well-known bimodal-HB clusters, NGC 1851 and NGC 2808, are brieÑy analyzed. While the HB morphology of NGC 1851 can also be reproduced with a unimodal mass distribution assuming a large mass dispersion, the same is not true of NGC 2808, for which a bimodal, and possibly multimodal, mass distribution seems deÐnitely required.The problem of gaps on the blue HB is also discussed. Applying the standard Hawarden and Newell s2 test, we Ðnd that the NGC 6229 gap is signiÐcant at the 99.7% level. However, in a set of 1000 simulations, blue-HB gaps comparable to the observed one are present in D6%È9% of all cases. We employ a new and simple formalism, based on the binomial distribution, to explain the origin of this discrepancy, and conclude that HawardenÏs method, in general, substantially overestimates the statistical signiÐcance of gaps. Paper I). showed that the horizontal-branch (HB) morphology of this cluster is characterized by two peculiar properties : (1) A distinctly bimodal distribution in B[V colors, consistent with the relatively small number of RR Lyrae variables, compared to the blue HB and red HB populations ; and (2) at least one "" gap ÏÏ on the blue HB, as previously noted by Fullton, & Trammell Carney, (1991). Bimodal-HB clusters are relatively rare, as are clusters with gaps on the blue HB. NGC 6229 is one of only four known casesÈthe others being NGC 2808, NGC 6388, and NGC 6441Èwhere these two anomalies are simultaneously present. As argued by many authors, an understanding of the nature of the detected peculiarities in "" bimodal ÏÏ and "" gap ÏÏ clusters would be of paramount importance for understanding the nature of the second parameter phenomenon (see, e. for producing HB bimodality in the speciÐc cases of NGC 6229, NGC 1851, and NGC 2808 ? (3) Are gaps on the blue HB a natural consequence of stellar evolution, as claimed by some authors ? (4) What is the statistical signiÐcance of gaps ?In this paper, we present extensive synthetic HB simulations for NGC 6229. We begin in the next section by laying out a proposed nomenclature for both deÐning and di †er-entiating "" bimodal ÏÏ and "" gap ÏÏ clusters. In we describe°3, the theoretical proc...