Should Full Text Filter Daemon Service be a cluster resource? Our newly installed and configured SQL Server Always On Availability Failover Cluster with SQL Server 2016 Enterprise Edition runs with four instances and six nodes. It includes the DB Engine Service and the Agent Service in each Cluster Node's resources. Everything works fine.
But now we figured that the fill-text Filter Daemon Launcher (FTFDL) service exists on each of the nodes and is randomly running, independant if the fact where the Sql-Instance is currently running. Some nodes have four FTFDL services running, while only one instance is located there. Others have one or two of them running.
Question: Should we add this service as a cluster resource? Why is it getting started and stopped abviously randomly on the failover cluster instances resutling in multiple services active without the relevant instance active? What is best practice here?
The Full-Text-Search daemon launches as required, and is triggered by the SQL Server engine itself.
So, in short, you don't need to add the Full Text Filter Daemon Launcher as a resource in a SQL Server failover cluster.
From the Docs page concerning Service Account settings for the Full Text Filter Daemon Launcher:

Make sure the SQL Server service group has permissions to the SQL Full-text Filter Daemon Launcher service account. During the installation of SQL Server, the SQL Server service group is granted default permission to manage, query, and start the SQL Full-text Filter Daemon Launcher service. If SQL Server service group permissions to the SQL Full-text Filter Daemon Launcher service account have been removed after SQL Server installation, the SQL Full-text Filter Daemon Launcher service will not start, and full-text search will be disabled.