Integrated sensing and communication (ISAC) emerges as a promising technology for B5G/6G, particularly in the millimeter-wave (mmWave) band. However, the widely utilized hybrid architecture in mmWave systems compromises multiplexing gain due to the constraints of limited radio frequency chains. Moreover, additional sensing functionalities exacerbate the impairment of spectrum efficiency (SE). In this paper, we present an optimized beam pattern modulation-embedded ISAC (BPM-ISAC) transceiver design, which spares one RF chain for sensing and the others for communication. To compensate for the reduced SE, index modulation across communication beams is applied. We formulate an optimization problem aimed at minimizing the mean squared error (MSE) of the sensing beampattern, subject to a symbol MSE constraint. This problem is then solved by sequentially optimizing the analog and digital parts. Both the multi-aperture structure (MAS) and the multi-beam structure (MBS) are considered for the design of the analog part. We conduct theoretical analysis on the asymptotic pairwise error probability (APEP) and the Cramér-Rao bound (CRB) of direction of arrival (DoA) estimation. Numerical simulations validate the overall enhanced ISAC performance over existing alternatives.