The fundamental problem of acting in opera is how to balance two opposing things: the need to draw upon real human behaviors and emotions and the alienating element of the music. A Method-based actor in a play is trying to "live truthfully" at all times on the stage. Using the imaginary circumstances of the play, the actor is ideally immersed in a separate reality right in front of our eyes. The actor listens honestly, responds honestly, and lets the performance develop from there. In rehearsal, the actor speaks when it feels right to do so, and in a manner that arises from the truth of living in that moment. No pantomiming or artificial gesture is needed to express this truth, anymore than you would need to externalize something right now to demonstrate to an audience that you are reading this sentence. It's enough that you're actually reading it, nothing need be enhanced or added.
I have seen theatre directors, really fine ones, try to get singing actors to master these skills quickly and to apply a rigid form of it to their performances. The result is usually mixed at best: singing actors standing in a totally still manner, "speaking" the music naturally, while clearly feeling that they are going against the grain of their instincts as performers. The actors invariably feel trapped and the performance is stilted.
Here are some of the reasons the performers probably feel trapped. 1) As singers, they have little ability to decide on tone of voice and the timing of their deliveries, as those choices are dictated by the vocal line, so they are at odds with their natural impulses. 2) While singing, the body is engaged in a difficult activity that requires stamina and focus, and which, moreover, pulls them away from the sensation of existing normally in the real world. 3) The music demands visual interpretation of some kind, and the actors feel they have to deliver this somehow, through gesture and movement. This last is the cause of much terrible acting in opera, all of it with the best of intentions.
So that's the dilemma the singing actor faces. On the one hand, the Method and it's edict to "live truthfully under imaginary circumstances." On the other hand, the music leading the actor away from any feeling of real life conditions.
I believe that the singing actor is also tasked with having honest insight into the human condition, and not just through vocal technique. The singer, too, is required to embody the character in the moment, not as a caricature but as a real person.
A marriage of kinds is possible, as some of our finest performers have shown. For an example, see the video above of Maria Callas singing Bellini's Norma. She gestures hardly at all, and never seems to be trying to "show" anything. Rather, one gets the feeling that she is merely speaking text, candidly and with feeling. The result is far more riveting than if she had attempted to fill the long lines with physical business for entertainment's sake.
So, how can a singer marry the two? Many great singing actors have talked about the importance of keeping the emotional intent present in the singing, even during practice sessions. As singers, we get so involved in the technical aspect that we lose sight of the point! Put the emotion in as a sort of game. Play! If play is lost from the process, it becomes a gymnastics routine, rather than an act of expression.
As a part of that process, we have to remember that part of investing emotion into our singing is finding out how those emotions really affect us and our behavior. There are many ways to do that, from acting classes and books on acting to simple self-observation.
We singers can't be afraid to explore the truth of our behaviors and feelings any more than actors are afraid to do so. We draw on them just as much.