The battery charging lights on the AYOpro case show up for a few seconds and then they shut off. Is that normal behavior?

This is a normal behavior of the AYOpro case and its battery indicator. When you make a connection (either between the case and a power source or between the wearable and the case when laying the wearable inside the case), the battery light indicator would blink for a few seconds to show there is a connection created and then it will shut off to preserve the battery. However, once you have made a charging connection, the charging process will continue (even though it is not blinking unless you tap on the battery light indicator) until full charge.