How do I downgrade node or install a specific previous version using homebrew?
These days if you want to install a different version of node you do it this way:

First search for your desired package:

brew search node


This might give you the follow results:

heroku/brew/heroku-node ✔
llnode
node@10
nodebrew
leafnode
node ✔
node@8
....


And then install the desired version:

brew install node@8


Also remember that you can install more than 1 node package at the same time, but you cannot have them available at the same time. So if you have the latest/generic node package already installed you need to unlink it first:

brew unlink node


And then you can link a different version:

brew link node@8


For some older node versions (which are keg-only), it might be required to link them with the --force and --overwrite options:

brew link --force --overwrite node@8