Today i have discovered something which can be interresting for people who have both DragonWrath and Ti'tahk.
I just tried with my warlock to cast some dots without DW equiped. After placing the dots, i have equiped my DragonWrath and i have discovered that his effect worked, whereas i didn't put the dot when the staff was in my hand.
I also asked a friend who got Ti'tahk (the staff from Madness) to try to activated the haste proc, and then put the staff in his bags. It resulted that the proc was still on him during the time remaining.
So my idea his that if you have the 2 staff you can use them wisely by switching between them. For exemple When you want to refresh your dots you can equip Ti'tahk, and then when you have to cast bolt you can switch back to your Dragon Wrath.
With a bit of luck your Ti'tahk will activate his proc.
It could be usefull too if your weapon have more spell power than your Dragon Warth, because if you use your dots with the most powered staff, your dots will still have this power, and when you will switch back to DW your dots will also have the chance to proc twice.
I imagine that Ti'tahk works with an internal CD, so it can be also interresting to switch between your weapons only when this CD end. I bet that this idea is better than my previous one
But there is just one thing that you can don't like: when you switch between your weapons, this will count as a GCD, so you will have to wait 1sec everytime you will switch. So you will switch twice to go back to DragonWrath, it will result to loose 2 GCD...
I don't think it's a normal game mechanic, because if you compare weapon with a trinket, when you try to use a trinket and move it back to your bag, the effect of the trinket will stop, but for the weapon it will persist until the end of the proc.