I would posit that sometimes the key a picture is appearing non-threatening to your subject. This is certainly true when humans are involved but even more so when the target of your hunt is one known for it’s short lifespan and frequent run-ins with flyswatters.
On a sunny day in June I chased this monarch of the potato salad around Laura’s back porch for the better part of an hour. Eventually patience won out over fear or else I just got the sun in the right place to blind him. Either way, he was worth the chase. Unfortunately, since at the time I didn’t fully understand the role of the aperture size in photography, the focus is a bit soft in places. Oh woe looking back at what we could have done had we just known better.