You need to see it interactively rather than scanning chat flying by at a rate of knots during battle. A seperate chat tab for it takes up too much space on the screen and unless you make it very large, you won't see things happening unless you're watching it all the time - which is impractical when your main attention needs to be on the battle.
Changing target to the pet to see what's on it doesn't work effectively because your target needs to be the mob you or your group is fighting. You only want to change if you need to do something about it - such as cure it.
Implied target works only as long as the pet is the target of the mob you're fighting. Soloing this is mostly OK - although not always. While grouping this is hardly ever the case.
Adding the icons to the pet window under its health bars would allow the pet user to see at a glance what's going on with his pet, which would be the optimum solution.
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