Installing a SQL Server patch on a node within a 2-Node FCI
The way we go about SQL patching and windows updates for a 2 node cluster is.


In Failover Cluster Manager, remove the node you want to patch from the Possible owners (makes sure it cant failover to this node until you are ready)
Patch the inactive node
Re-add the node to the Possible owners
Failover to the inactive node
Leave this running for a day or two to make sure there are no issues
Remove the first node from the Possible owners (now the inactive node)
Patch the now inactive node
Re-add the node to the Possible owners
Fail-back


As long as your inactive node does not have the Quorum or Cluster Group patching or rebooing the inactive node should have zero impact.

The easiest way to make sure the node you want to patch does not own anything is using Powershell.


Open Powershell
Run the following command "import-module failoverclusters"
Then run "get-clustergroup"


The output will show you what resources you have in the cluster and what node the currently live on.

Here is an article from MS on the topcic, https://support.microsoft.com/en-au/kb/958734.