Other Parts Discussed in Thread: OPA4277, OPA277
Is there are recommended configuration for 5962-16209 when a channel is not being used?
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The same rules will apply for this device as pretty much any other amplifier - it's best to place unused channels into a buffer configuration and buffer a voltage around midsupply. I would suggest a pair of 50k resistors to create the divider, in order to minimize the wasted current, and a 100 ohm feedback, to add a little phase margin. The feedback and input divider resistances should protect the inputs/clamps in case of an SET. The aforementioned component values will give you about 47 degrees phase margin with 10pF parasitic capacitance.
If you change the values around just be sure to do a quick sanity check for stability, my first instinct was to use 100k divider resistors but that resulted in a marginally stable circuit. Same thing if you anticipate higher parasitic resistance, it's always good to double check!
Unfortunately I don't have a ton of information about the device that I can share from a process/technology perspective. However, I do know that the OPA4277 is fabricated on a bipolar process, with a bipolar differential input pair that includes input bias current cancellation circuitry (source). Hope that helps!