There is some discussion about permafrost in the CLM5 paper (section 4.5):
David M. Lawrence, et al., 2019: The Community Land Model version 5: Description of new features, benchmarking, and impact of forcing uncertainty.
Journal of Advances in Modeling Earth Systems, 11, 4245-4287.
https://doi-org.cuucar.idm.oclc.org/10.1029/2018MS001583.
and in the CLM4 paper (section 4.6):
In the CLM4 paper, near-surface permafrost extent was defined as the integrated area in which at least one soil layer within the uppermost 3.8m remains below 0C through the year. So one could use the history variable TSOI to diagnose this.
Another variable of interest is "ALT" (active layer thickness; the depth to which permafrost soils thaw each summer). See src/biogeophys/ActiveLayerMod.F90.
TSOI should be available in any configuration. ALT is available in BGC mode and can be turned on in SP mode as well.