How to Force Failover to Second Node

You may also create port specific monitors (alias port definition) and assign them on node level. By default the 'availability requirements' is set to 'all'. So if one monitor fails, the node will be marked down. The node acts as parent object in all pools and you will observe a failover to node.

[root@bigip_a11:Active:Disconnected] config  tmsh modify cli global-settings service number
[root@bigip_a11:Active:Disconnected] config  tmsh list ltm monitor http monitor_port_80
ltm monitor http monitor_port_80 {
    defaults-from http
    destination *:80
    interval 5
    send "GET /\\r\\n"
    time-until-up 0
    timeout 16
}
[root@bigip_a11:Active:Disconnected] config  tmsh list ltm monitor http monitor_port_8081
ltm monitor http monitor_port_8081 {
    defaults-from http
    destination *:8081
    interval 5
    send "GET /\\r\\n"
    time-until-up 0
    timeout 16
}
[root@bigip_a11:Active:Disconnected] config  tmsh list ltm monitor http monitor_port_873
ltm monitor http monitor_port_873 {
    defaults-from http
    destination *:873
    interval 5
    send "GET /\\r\\n"
    time-until-up 0
    timeout 16
}
[root@bigip_a11:Active:Disconnected] config  tmsh list ltm node node25
ltm node node25 {
    address 10.131.131.25
    monitor monitor_port_80 and monitor_port_8081 and monitor_port_873
    session monitor-enabled
    state checking
}

Are you looking for a pure HA setup?

I.e. all traffic is generally balanced to one node only, sticks there and reselection only applies if it fails and from now everything should stick to the alternative node?

In this case you can use priorities and combine it with 'destination address affinity'.

Even if this sounds a bit odd, but it works fine. The persistence table will show a single entry with target of virtual IP and selected poolmember. In case of reselection this single entry changes accordingly.