Plant secondary metabolites as thymol and carvacrol undergo glucuronidation and sulfation in liver, intestine and kidney. There are several isoforms of enzymes involved during this phase II of biotransformation.
I dont think there is any direct report on query you arise on thymol and carvacrol. But it is confirmed both give strong antioxidant action and you may corelate your study with the simlar study by getting full paper of this reference.