Testing for heterogeneity of total variances of MZ and DZ pairs

The long and short of it is that you would fit a model to your data in which the phenotypic variances for MZ and DZ twins are two different free parameters, and then fit another in which the phenotypic variance is the same free parameter for both groups. The change in -2logL between the two models is a likelihood-ratio test statistic, asymptotically distributed as chi-square on one degree of freedom.

I'm attaching a script from the 2016 Boulder Workshop. You'll need to adapt it to your purposes, but hopefully it's enough to get you started.