The gold standard is a precious metal delivery service

On Targeting the Price of Gold

So although a central bank may target the price of gold, or adhere to a gold "price rule," by doing so, it creates a "pseudo" rather than a "real" gold standard. Having a real gold standard, in contrast, doesn't call for having a central bank at all, as many past examples make clear.  Indeed, so far as many fans of the classical gold standard (including this one) are concerned, central banks have mainly served to muck things up.

George Selgin has it right. The rue purpose of a gold standard is to eliminate the central bank.  What remains is simply a gold pick up and delivery service, a logistics network for precious metals.

If precious metals are a critical input to the economy, then a gold delivery service satisfies the Lucas critique as a precious metal delivery network  matches the economies demand to have precious metals delivered, there is no mis-specification, no unbounded leaks.  The Lucas critique demand the total bound solution be included, the quantum mechanical version.

This is an old topic.  Alt-M covered the concept of a precious metal delivery services, it is a very simple mechanism, having little to do with currency banking and more to do with valuable paper shipping 'tickets used to insure deliveries.  The Lucas critique would specify that precious metals must generally be the first constraining input to the economy, thus it defines the boundary conditions of a quantum mechanical pricing system.  Quantum mechanical means, gold is conserved and a necessity, but delivery uncertainties remain, and are well known. Well known uncertainties are hard bound, a Plank's constant. Being well know, the gold market will quantize shipments to stay within the bound.