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We report the results of a search for 12.2‐GHz methanol maser emission, targeted towards 113 known 6.7‐GHz methanol masers associated with 1.2‐mm dust continuum emission. Observations were carried out with the Australia Telescope National Facility (ATNF) Parkes 64‐m radio telescope in the period 2008 June 20–25. We detect 68 12.2‐GHz methanol masers with flux densities in excess of our 5σ detection limit of 0.55 Jy, 30 of which are new discoveries. This equates to a detection rate of 60 per cent, similar to previous searches of comparable sensitivity. We have made a statistical investigation of the properties of the 1.2‐mm dust clumps with and without associated 6.7‐GHz methanol maser and find that 6.7‐GHz methanol masers are associated with 1.2‐mm dust clumps with high‐flux densities, masses and radii. We additionally find that 6.7‐GHz methanol masers with higher peak luminosities are associated with less dense 1.2‐mm dust clumps than those 6.7‐GHz methanol masers with lower luminosities. We suggest that this indicates that more luminous 6.7‐GHz methanol masers are generally associated with a later evolutionary phase of massive star formation than less luminous 6.7‐GHz methanol maser sources. Analysis of the 6.7‐GHz associated 1.2‐mm dust clumps with and without associated 12.2‐GHz methanol maser emission shows that clumps associated with both class II methanol maser transitions are less dense than those with no associated 12.2‐GHz methanol maser emission. Furthermore, 12.2‐GHz methanol masers are preferentially detected towards 6.7‐GHz methanol masers with associated OH masers, suggesting that 12.2‐GHz methanol masers are associated with a later evolutionary phase of massive star formation. We have compared the colours of the Spitzer Galactic Legacy Infrared Mid‐Plane Survey Extraordinaire (GLIMPSE) point sources associated with the maser sources in the following two subgroups: 6.7‐GHz methanol masers with and without associated 12.2‐GHz methanol masers; and 6.7‐GHz methanol masers with high‐ and those with low‐peak luminosities. There is little difference in the nature of the associated GLIMPSE point sources in any of these subgroups, and we propose that the masers themselves are probably much more sensitive than mid‐infrared data to evolutionary changes in the massive star formation regions that they are associated with. We present an evolutionary sequence for masers in high‐mass star formation regions, placing quantitative estimates on the relative lifetimes for the first time.