I was trying to do something similar a few days ago with a hierarchical Gompertz model implemented through brms - see thread here: Hierarchical Gompertz model
I gave up in the end as no matter what I tried I could not quite make it work. I think there might be an identifiability problem with the equation - the equation has 3 fixed effect parameters and one variable. But, I don’t know quite so much about identifiability so its just a guess.