Acetyl CoA inducing gluconeogenesis: in the liver, pyruvate carboxylase is activated by acetyl CoA during fasting. Think about what happens during fasting? Excessive lipolysis creates a flood of acetyl CoA (also NADH + ATP) which will happen in a state with high glucagon or low insulin. Notice that acetyl CoA also inhibits pyruvate dehydrogenase (shunting towards gluconeogenesis).
Citrate: If you notice, citrate not only stimulates gluconeogenesis, it also inactivates the glycolytic pathway (via inhibition of PFK-1). Again, like the previous scenario, hepatic oxidation of fatty acids will lead to increased ATP, acetyl CoA, and citrate.
AMP: In a situation with high AMP, you want to stimulate glycolysis for quick energy while NOT making glucose which requires energy (ATP). AMP inhibits fructose 1,6 bisphosphatase. Think about gluconeogenesis, it requires ATP and NADH to make the glucose (which is brilliant because they are produced in large quantities during fasting state via beta oxidation of FA). Having lots of AMP means you don't have lots of ATP, so AMP should inhibit gluconeogenesis.
sources: RR biochem + lipincott biochem