The cluster is also notorious for problems with the connectors to the bike's wiring harness, on the back.
Pull the connectors, remove the cluster, and carefully clean the pins.
There are also connections within the cluster that may be at fault, but clean the easy ones first and see if that helps. People swear by both Stabilant 22 and DeOxit as contact cleaners/enhancers - they don't just get the grime off, they actively promote conduction when you put the connectors back together.
Lastly, the weirdness of the gear indicator and neutral light could also suggest problems with the gear position indicator switch, which is screwed into the back of the transmission. Since you're having a couple other, unrelated items in the cluster go out, that points more toward the cluster end of the wiring, but it's also possible there's more than one thing going on.