We have mapped the Heiles cloud 2 region in the Taurus molecular cloud complex with (HCO+)-C-13 (J = 1-0), CH3OH (J(K) = 2(0)-1(0) A(+)), and (CS)-S-34 (J = 2-1) lines. Dense gas traced by the mapped lines with critical densities higher than 10(4) cm(-3) is concentrated in four condensations, that is, the TMC 1 and TMC 1C filaments, L1527, and TMC 1A. We have found that the three emission lines have remarkably different spatial distributions. The (HCO+)-C-13 emission traces well dense cores harboring protostars, while the CH3OH emission is weak toward the protostars and is rather enhanced toward cores without protostars. We found that there are two starless cores with enhanced CH,OH emission at the northwestern ends of the TMC 1 and TMC 1C filaments, toward which the (HCO+)-C-13 emission is barely seen. On the basis of the analyses using the large velocity gradient (LVG) model, we show that the CH,OH abundance relative to (HCO+)-C-13 is, enhanced by up to 1 order of magnitude in the cores without protostars. The (CS)-S-34 abundance relative to (HCO+)-C-13 also shows a similar trend to that of CH,OH. Such an abundance variation between (HCO+)-C-13 and CH3OH and (CS)-S-34 can be explained in the scheme of time-dependent gas-phase chemical evolution, which predicts that CH3OH and (CS)-S-34 are abundant in the early stages of chemical evolution and become deficient in the later stages. A comparison of the spatial-velocity structures in TMC 1 observed with the three molecular lines suggests that this cloud consists of multiple components with different velocities and different chemical compositions along the line of sight.