Brian Molko does have tattoos.
He has one in his right hand which is a symbol of sobriety. Having that tattoo is a great deal to him. It’s etched into his skin, and it’s a part of him thus, he will carry it to his grave. It’s an emblem of some kind of commitment. No matter what I do, it’ll still be a part of my identity.
Likewise, there is also another tattoo on his arm that reads “This too shall pass”. What’s more, he even once talked about having a little demon tattooed on his shoulder.