What is "cytosolic signal impedance"? This is the first time I have come across this term.

The cellular mechanism of action of insulin can generally be grouped under a "second messenger system". This means that the signal its self (initiated by the insulin molecule) does not actually enter into the cell, but is transduced from the outside to a signal cascade on the inside (cytosolic side).

As such, a receptor system will have an extracellular component, a transmembrane component, and a cytosolic component. Cytosolic impedance (of the insulin signal) can occur as a function of the expression of a particular factor (protein) which interferes with the signal transduction on the cytosolic side of the receptor.

If you want to read the nitty gritty, here is a decent reference:

https://www.ncbi.nlm.nih.gov/books/NBK378978/

Oh, I understand, so the impairments in beta cell function are a secondary, later, consequence of insulin insensitivity, which typically is at first driven by... what exactly?

Beta cells are thought to be impaired by an autoimmune (or autoimmune like) attack on beta cells, though I think this is still up for debate. If they get taken out, you do not secret insulin, this is often a characteristic of a type 1 diabetic (vs. a type 2 in which you tend to see a decrease in the sensitivity down stream, in some cases as described above.)