Glenn,
I have seen many various methods to empirically determine secondary current ratings of unknown transformers but a lot of them apply to either single secondaries or the larger utility distribution transformers.? If you have a working transformer with known secondary voltage(s) I have usually used a simple and sometimes less-than accurate method of applying a load to the secondary until the voltage drops 10-15% then measuring the current.
Usually the transformer manufacturers will specify the rated output voltage near the full load condition and the output is obviously much higher in an unloaded state.? But for smaller transformers one must also take into consideration of possible core saturation when nearing a full-load condition.? That can be observed with an oscilloscope while applying loads to the secondary.
Other numerous approaches taken have been taken and I am sure others will weight in on them but some either are not indicative of a true current rating for those transformers? with multiple secondaries or may be destructive when attempting to test. This is especially true if the transformer contains buried thermal fuses in the windings that may open upon an overload condition.
Contacting tech services of one of the major transformer manufacturers may also shed more light on how to determine currents.? As a sidebar I once did a design on a power supply and contracted with a small local manufacturer to produce the required transformer for the application.? The company actually was in the business of producing inclinometers for off-road vehicles but the engineer who worked there loved transformers so the company let him set up a small manufacturing facility to produce them.? The guy was a wealth of knowledge on transformer design and became quite a source of education on the subject. After all of these decades I don't see the company around anymore so off-road enthusiasts apparently trust the capabilities of their vehicles until they tip over.
Greg