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Related to Blind Obedience.
Related, I agree, but a bit distinct. This isn't so much about loyalty as it is an absence of critical thinking.
The troupe codifier, I would think, would be Amelia Bedilia.
Amelia Bedilia is Literal-Minded — she's not blindly following orders, she's misunderstanding them.
Currently Working On: Incorruptible Pure Pureness
If it's framed as the character believing they're duty-bound to obey all orders, no matter how strange they may appear, it would be Honor Before Reason.
(Fun fact: Back in the bad old days when it was acceptable to name tropes after characters, the trope now known as Literal-Minded was just called "Amelia Bedelia" instead.)
I didn't write any of that.
^They even use dear Amelia as the page image on Literal-Minded.
To get on topic, have you looked at Incapable of Disobeying?
Edited by PCD
Is there a troupe involved a character following directions as if they were a robot, even if those directions make no sense under the circumstances. This would be distinct from "Just following orders," since we're not necessarily talking about morally objectionable actions. Just directions that obviously don't make sense, and that any reasonable person would, at least, question. Often played for laughs.
Some examples:
1. In an episode of Big Bang Theory, Sheldon tries to reduce "making a friend" to computer flowchart, which he follows literally when trying to make friends with Kripkie. Hilariry ensues when he ends up in a perpetual loop.
2. In Superman III, a computer is programed to send a message to every oil tanker in the Atlantic Ocean, ordering them all to sail to the middle of the ocean and "await further orders." All but one ship complies without question.
3. In a Bugs Bunny cartoon, Bugs defeats two cowboys by becoming a square dance caller and direction them to do things like bash each other over the head, dance into a lake, etc.
4. In Die Hard 2, after being taken over by a group of terrorists, an Air Traffic Control tower orders all the planes to hold, indefinitely. They all do so, without question, even to the point of coming dangerously close to running out of fuel. In the real world, long before being in danger of running out of fuel, the pilots would have simply gone to another airport.
5. Averted in the opening scene of Wargames, when two airmen working in a missile silo suddenly and unexpectedly receive orders to launch their missiles. The junior threatens the senior with a gun simply because the senior wants to call someone to confirm that they have REALLY been ordered to launch their missiles.
Edited by wsmith76