I ALWAYS check the F2 mode and do a wide sweep around looking for objects. I have had nothing but bad luck with sun battles, but I love them! They are so much fun! Other objects are my friends.
Dunno how the F1 and Sun/asteroid looks, but while I do use that sometimes, I dont use it to look around all the time.
Remember, once you spot the sun, hit Ctrl+5-8 to lock it.
Helps from heading into it... Not that it's ever helped me, hehe.