I'd like to know the precise meaning of "conscientiously" in this excerpt from the chapter five of The Great Gatsby:
Amid the welcome confusion of cups and cakes a certain physical decency established itself. Gatsby got himself into a shadow and while Daisy and I talked looked conscientiously from one to the other of us with tense unhappy eyes. However, as calmness wasn’t an end in itself I made an excuse at the first possible moment and got to my feet.
The afternoon in which Nick arranges for Gatsby to meet Daisy is a nerve wracking one for Gatsby. He has been worried that the meeting must go absolutely perfect. Gatsby made sure that the flowers were ordered, that Nick's lawn was cut, and that he, himself, looked the part of someone who is meeting his dream. When Daisy does not show up until exactly 4:00, or a couple of minutes before it, Gatsby is almost deathly ill out of nerves. When Nick goes out to greet Daisy, Gatbsy struggles to find a perfect posture, something that would make him appear to Daisy how she appears to him. An impossibility in its own right, Gatsby tries to lean on a mantelpiece, but only succeeds in leaning against an old and defunct clock, causing it to fall to the ground and break into pieces.
After this slight awkwardness, the afternon tea continues. To a great extent, Gatsby is envious of how easy Nick is able to banter freely with Daisy. Gatsby remarks that it has almost been five years since Gatsby has seen Daisy. Remembering the exact time that has elapsed takes both Nick and Daisy by surprise, but it reflects how much he idealizes Daisy. The fact that he cannot speak to Daisy so easily along with how stressed he feels by the weight of expectation causes him to almost be a "third wheel" in the scene.
It is for this reason that he "conscientiously" watches both Daisy and Nick. In this setting, "conscientiously" can be defined as almost painstaking detail, and in a scrutinizing manner. He watched both freely talk, doing what he wished he could do at that moment. His watching both of them with a painstaking approach reflects how he is so very close to his dream, but also reflects the horrific anticipation and weight of expectation that accompanies such proximity.