Using Target of Target to attack what the tank is works ok for a healer who wants to throw out an occasional attack without changing their targeting setup, but isn't very good for DPS classes. DPS should usually target an enemy and keep hitting that same enemy until its dead. The tank, on the other hand, is likely to be cycling around between all the enemies in order to maintain hate on everything. Following the tank's target would spread DPS out too much when it should instead be focused on Target 1.
I think a combination of adding all engaged mobs to the enemy list (as Thalassocrat suggested in the opening post here) and adding the marking signs to the enemy list (as Bixby suggested) would make targeting the right mob far easier for both DPS classes and tanks.
It gets annoying when my character is just standing there doing nothing because I'm busy hitting next-next-next-next-next-next-next-next (left or right on controller, I guess tab would be the equivalent on PC) just hoping target 1 (or 2 or whatever we're on by that point) will eventually show up as targeted so I can start attacking.