This article presents a method for quantification of methanol and ethanol integrated in the same gas-chromatographic run with a quantification of gases dissolved in mineral oil, making it an integrated tool in transformer diagnostics. The results of aging experiments at 120 °C and 60 °C of Kraft paper, copper, barrier, and pressboard immersed in mineral oil, as well as the aging of thermal upgrade paper in mineral and natural ester oil at 140 °C are presented, in order to investigate correlations between different aging markers and to evaluate their partitioning between oil and cellulose at defined conditions. The results of partitioning experiments at 60 °C showed that re-absorption of methanol from oil to the cellulose materials is faster than the re-absorption of furans. This means that methanol is a paper-degradation marker that can be used in diagnostics over shorter equilibrium times and for the detection of developing faults at broader temperature ranges. Furthermore, a statistical overview of methanol concentration from a database and two transformer fault diagnostic cases are presented. Therefore, in addition to an analysis of gases dissolved in oil, the use of methanol and ethanol in transformer fault and failure investigations should be explored and verified through transformer fault investigations and postmortem analyses.