In migration, birds use a variety of navigation aid; sun, stars, magnetic fields and probably others we don't know about. Some birds migrate for days continuously so can not use the sun at night. Over head clouding will not prevent them from flying at night but the electricity from storms seems to confuse them and many birds have landed on ships out in the ocean during a storm and take off again when it subsides. They appear to be able to detect bad weather ahead and fly lower/higher so it is believed that the electricity with bad storms confuses them.
I do not for a minute believe that it was the eclipse that caused the deaths.