I've always thought it's kind of weird that TotG has 2 seperate internal cooldowns. My proposal is to get rid of the item's cooldown altogether, and instead base the mana gain on the amount of mana spent.
The new tear might be something like "you gain permanent mana equal to 2% of the mana you spend" (but still have the 750 cap). This change would eliminate the need to time your spells with the tear's internal cooldown(s) and would allow champions with high mana requirements to benefit from it even if they don't cast spells in rapid succession, such as with Swain. Champions like Karthus with a high spellcast rate would still get roughly the same benefit, since low-cooldown spells also tend to have lower mana costs.
Archangel's staff could just use 3% instead of 2%, and Manamune could still use attacks but not have a cooldown (with your attack speed effectively becoming the cooldown).
The exact percentage could be subject to change, I just think that champions like Swain or Anivia with high mana requirements shouldn't be stuck with a slower buildup speed than other champions with those mana requirements like Zilean and Karthus.
Edit: Now that I think about it, Tear should probably be closer to 5% or 6% so it averages the same 4 mana/spell.