Tag Management Systems were developed in order to support website publishers in installing multiple third-party JavaScript scripts (Tags) on their websites. Google developed its own TMS called ``Google Tag Manager'' (GTM) that is currently present on 42\% of the top 1 million most popular websites. However, GTM has not yet been thoroughly evaluated by the academic research community. In this work, we study, for the first time, the Tags provided within the GTM system. We propose a new methodology called ``detecting privacy leaks in isolation'' and apply it to multiple Tags to analyse the types of data that Tags collect and contrast them to the legal and technical documentation, in collaboration with a legal expert. Across three studies - in-depth analysis of 6 Tags, automated analysis of 718 Tags, and analysis of Google ``Consent Mode'' - we discover multiple hidden data leaks, incomplete and diverging declarations, undisclosed third-parties and cookies, personal data sharing without consent and we further identify potential legal violations within EU Data Protection law.