Until he had worked out this solution of the situation he had determined to leave.
Betty's deceit had disgusted him.

But now, though there were faults in the structure of the solution he had worked out, he was certain that they intended working along those lines, and he was now equally determined to stay and see the thing out.
Of course, Taggart was trying to make a fool of Betty--that was all too evident.

A man who has serious intentions--honorable intentions--toward a girl does not talk about her to his friends as Taggart had talked.
Taggart did not care for her; he was merely planning to gain her confidence that he might gain possession of the money and the idol.

The very fact that he was meeting Betty secretly proved that she had not given him the treasure.

Perhaps she had doubts of him and was delaying.
Yes, that was the explanation.