Can someone tell me why my low voltage lights are reading high current at the switch?
First, your clamp-on meter is probably not very accurate at such low currents. Check the specs - it's probably good for something like +/-3% of full scale, which would likely be 40A or more. That's an allowable error of +/-1.2A.
But the real issue here is power factor. Measuring current and voltage separately allows you to calculate "apparent power" in volt-amps, but you do not know the phase relationship of the voltage and current waveforms. They are never perfectly aligned, and the phase shift between them results in less "real power" than the volt-amp calculation indicates. This difference is called the "power factor". Transformers that are under-loaded have very poor power factors, as do some electronic devices. So if the transformer for this lighting is rated for much more than the 13W load, you can expect the volt-amp measurement to be much higher than the real power being consumed. Similarly, if it's a cheap electronic lighting transformer, the power factor may be very low. To measure real power you need a wattmeter that accounts for the power factor.