I tested several options of auto keying, expecting keys to be generated in the Rotation Order channel. However, all keying sets only generate keys for transforms and not for rotation orders. The Whole Character keying set is fantastic because it generates keys for properties as well as transforms, but it was disappointing as it doesn't work for rotation order.
If you're dealing with multiple actions in one blend file, you'll also need to create a key for the rotation order as well. In most cases, quaternions work fine, but sometimes you need an euler. Is there any special reason for auto keying options to exclude rotation order? If not, is there an option I'm missing?