Is there a single word or phrase to describe a context-less option for "manual" or "automatic"?

Solution 1:

I would go with control.

It gives the right sense of determining who is in charge of decision making: either a human (manual), or a machine (automatic).

Solution 2:

A very general term for this choice would be Mode

Solution 3:

Similar to answers above, I think a general "Automation" or "Automation Level" would be the description for effects gained by one of the choices you mentioned (anywhere from automatic to 'manual', or 'by-hand') and indicate that one was to select at which level one would expect to take or assign control.

Automation:

the technique, method, or system of operating or controlling a process by highly automatic means, as by electronic devices, reducing human intervention to a minimum.

Particularly, as it applies to the technique or method (or extent thereof) of controlling a system in automatic fashion.