So I'm using my own chart to understand this technique. I'm a good guinea pig because my Lagna Lord and AK are the same plant, which is in the third house with the fourth Bhava. My Lagna doesn't have a ton of aspects on it.
I was a little surprised to find that a focal fourth bhava is said to produce an emphasis on the pursuit of happiness. I have never really prioritized happiness until recently. It was just not my habit, I saw happiness as a product of my other projects.
However I have a very strong lifelong tendency to want to pursue things and then give myself permission to be happy. Once I learn that new skill, try out that class, have that experience, make that career change, etc. then I can be happy. That's a much stronger pattern in my life.
So it seems the focal bhava indicates the ultimate goal and the house indicates the framework within which the process takes place, from my understanding.
Would this be typically how the house placement might impact the expression of the focal bhava?
Yes, that is an accurate observation. Its human nature to thing, once this is done, I will be happy, but the house placement can answer the question as to WHAT this thing to be done is.