Coconut milk tastes bland
First off, that probably isn't the best brand of coconut milk. I've never been that impressed, and Cook's Illustrated's review agrees, saying it was "too 'liquid-y' and 'thin'". They like Aroy-D, Roland, Goya and Chaokoh better as of May 2017.

But on top of that, you probably got a lot of water from the eggplant. It's mostly water, and it releases plenty of it as cooking breaks down the structure. 

I might try stir-frying the eggplant first, or roasting if you prefer, then adding it to the curry at the end. That way the liquid will be pretty much just coconut milk.

If it still seems too watery, you could do the same for other ingredients. Chicken breasts can release some water, and peppers too, but nowhere near what you get from eggplant. This does let you make sure they're cooked exactly as much as you want, so you might like it regardless of the watery issue.

You can also always just add more curry paste. Often the ratios suggested on storebought curry paste yield a less flavorful curry than what you probably get in restaurants.



To answer your side questions: long cooking is fine, and you don't have to do anything special to coconut milk to make it work.