Ok, but either way - is writing data to both the replica and primary the way to go here - in order to be fault tolerant?
Again, saying "writing to both" is a misnomer since that's not what happens. But yes, list all known ES nodes in the elasticsearch output (and consider enabling the sniffing option) so that Logstash sends requests to any available node and lets the ES cluster figure out which node has the primary shard for each document that's to be stored. (For clusters sufficiently big to have master-only nodes it's a good idea to avoid those nodes.)