How can I tell what amperage a 12V rated electrical device will run at 5V?
From the datasheet:


The table in the datasheet specifies the module resistance to be 1.9 to 2.3 Ohms.
it gives a ball park figure. I say ball park figure because the current cannot be predicted exactly, as it depends on the temperature difference between the plates too.

The graph assumes one has constant current source. In OP case, i assume it is constant voltage source. Still, for a rough estimate, the graph serves good. 

The voltage difference generated as the effect of conductor with two different end is termed as Seebeck effect. it is similar to back EMF generated while driving a motor.

This generated voltage is directly proportional to the temperature difference between two ends. Such open circuit voltage is equal to the product of Seebeck coefficient and the temperature difference. Hence, thus higher the temperature difference, more will be the voltage generated. The Seebeck coefficient of metals are mentioned wrt platinum as standard second junction.

This voltage hence tries to reduce the current drawn by the Peltier (Lenz law) when the temperature difference is higher. Since the graph is presented for constant current source, one can see that higher the temperature difference, the voltage needed to maintain the given current is more.