How to safely connect unused opamp stable for gain of +2
When an opamp is not unity gain stable then you should not do this as this is the unity gain configuration:



simulate this circuit &ndash; Schematic created using CircuitLab
With the risk of oscillations and instabilities.
Your Case 2 could be an option but still, you'd have to check that it is really stable. I'm too lazy for that so here's what I would do. I would simply get rid of the feedback and use the opamp as a comparator:
So this is what I would do:



simulate this circuit
This applies a small input voltage (~280 mV) at the input. All opamps should be able to handle this for a very long time without issues. The output of the opamp will be pulled high. If swapping the inputs of the opamp is more convenient than that's OK as well, then the output will be pulled low. Since there is no feedback, there can be no oscillations and instabilities.