Commands executed in Gaia OS on VSX Gateway are logged into /var/log/messages file, but do not contain the VSID of Virtual Systems, in whose contexts these commands were executed.
Aug 10 10:43:53 VSX_GW shell: cmd by admin: cd $FWDIR
Aug 10 10:43:55 VSX_GW shell: cmd by admin: pwd
Aug 10 10:44:01 VSX_GW shell: cmd by admin: cphaprob state
By the current design, VSID is not logged.