Totally characteristic wave type operators naturally appear in cosmological black hole type spacetimes in General Relativity. We propose a parametrix construction for such operators using Mellin type quantization. We then deduce the index 0 Fredholm property which allows us to define resonances of these operators as the zeros of a Fredholm determinant. If time allows it, we will discuss how to use this method to numerically approximate resonances with control of the error.