Quick note to myself.
Having an environment where some services (LDAP, Radius, …) that the F5 needs to access are not reachable from the Virtual Server but only via the management interface can be tricky. Adding a specific route to the host in question will solve this.
The command where 10.0.20.10 is the server we want to reach and 10.0.10.1 the gateway for the management interface is:
tmsh create sys management-route 10.