hey this is my guide for if you want to play ap eazreal when mid is already taken.

pros:
-fun
-high skill cap
-low cooldown ult
-can help from a long range with ult
-high dps

cons:
-mana problems
-people think you are trolling
-no cc
-bad camp clear

start with golems or frog ask for a hard pull.
get red or blue afterwards

when you are lvl 3 you can essence flux yourself for the attack speed by jumping on it with arcane shift. this allows you to clear the camps faster.

jump in your opponent and kill him.
that is my advise.