A central feature of the equilibrating mechanism is a negative response of the desired real current account balance to movements in the real exchange rate. There is no evidence of such a response in the data presented here.
True or False?
The answer is false. The Canadian experience before World War I clearly provides evidence of a negative response of the current account balance to the real exchange rate. An enormous capital inflow into the country occurred, accompanied by a very large increase in the country's real exchange rate. It is reasonable to interpret this real exchange rate response as an equilibrating one---necessary to create a desired current account deficit equal to the desired inflow of capital.
Even if the relationship between the real exchange rate and real current account balance observed here is not present in the data, one cannot conclude that an adjustment mechanism of the sort postulated in the question was not present. Exogenous shifts in desired exports and imports will obscure the effects of real exchange rate movements in adjusting aggregate demand to aggregate supply---that is, the BT line may shift back and forth a lot as compared to the shifts in the vertical SI line.
Indeed, if the desired current account balance were to respond positively rather than negatively to real exchange rate movements, no equilibrium would be possible. The real exchange rate would go to zero or become infinite. For example, a shift of world investment into the domestic economy would raise domestic aggregate demand. The relative price of domestic output in terms of foreign output---the real exchange rate---will be bid up through either an increase in the domestic price level or an appreciation of the domestic currency in international markets. If the rise in the real exchange rate increases exports relative to imports, having a positive effect on the current account balance, aggregate demand will further increase, creating additional upward pressure on the real exchange rate and driving the economy further away from equilibrium.