The Fructose-1,6-Bisphosphate to Fructo-6-Phosphate step is reciprocally regulated by both allosteric and hormonal control.
The Pyruvate to Phosphoenolpyruvate step is reciprocally regulated by allosteric molecules.
The key regulation points are:
The carboxylase and dehydrogenase acting on pyruvate, and
The kinase and phosphatase acting on fructose-6-phosphate and fructo-1,6-bisphosphate, respectively.
They are the key point for regulation because the reaction and hard to reverse.
I cheated this one when I write this, the answer is PFK2/FBPase2
Here is my inference:
Glucagon indicates a low level of blood glucose (memonics - insulin, its 'enemy', signal the high level of blood glucose). With low level of blood glucose, we need to have more gluconeogenesis and less glycolysis.
Fructo-2,6-bisphosphate reduce the sensitivity of ATP to fructose-6-phosphate to fructo-1,6-bisphosphate step (I remembered this)
Fructo-2,6-bisphosphate thus promote glycolysis. In the case of low blood glucose, we do not want glycolysis, so we do not want fructose-2,6-bisphosphate.
Therefore Protein Kinase A phosphorylates and inactivate PFK2, it phosphorylates and activate FBPase2, both action is done to reduce the quantity of fructose-2,6-bisphosphate.
And then
Wikipedia confirmed my interference is correct.