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So I know that in glm(), with the Gamma family, one can get the dispersion parameter through the MASS package with gamma.dispersion() or can even look at the summary output as a quick estimate.

How does one get the estimate of dispersion in a Gamma GLMM?

Also, what is the interpretation of the variance/std dev in Gamma GLMM? Are these already in the CoV units or are they in the units of the original data?

What I mean is, when I read off the std dev in a Gamma GLMM, do I interpret that as the std dev with the same units as the response variable as in a regular LMM, or is it already a proportion?

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