The Dominant Personality
If Guil were Batman, Ros would definitely be Robin. Guil is clearly the leader and Ros is the sidekick. The analogy may sound stupid, but there's something more here. Ros and Guil are most definitely not Batman and Robin, or superheroes of any kind. More than that, they're not what you might call leaders – or even "active" people. They're spectators, and they almost always choose to let things happen to them instead of taking action.
This is important because, of the two, Guil is the leader. That is, he is the leader of his friend Ros, who is slightly more hapless and inactive than he is. Guil is thrown into this role, but he is not, in any way, suited to it. Guil is not a natural leader. By the third act, he laments that he's the one who always has to take charge:
GUIL: I'm sick of always making the running.ROS (humbly): It must be your dominant personality. (Almost in tears.) Oh, what's going to become of us! (3.106-107)
As Ros points out, Guil is the dominant personality. He has a bit of an ego. He often acts as if he's better than Ros and frequently criticizes his friend. For example, when Ros is going on and on about death, Guil cuts in and tells him savagely, "You don't have to flog it to death" (2.224). At times, it seems that Guil is more of a bully than a leader. He can be mean.
Yet, there's something painfully obvious here: Guil needs Ros as much as Ros needs Guil. He never admits this, but it's true. For one thing, how many other friends does Guil have? None. Who else would Guil talk to? Presumably nobody. Who comforts Guil when he is having a bad day? Ros. In Act III, when Guil is on the verge of tears after the pirates have left them high and dry, it's Ros that comes over to comfort him.
So, Guil is the dominant personality, but it is also more complicated than that. He acts as if he is so superior to Ros, and yet he can't of admit how much he needs him.
The Pseudo-Philosopher, who may or may not care about truth
From the very first scene with the coin toss, Guil is established as a questioner. In the stage directions at the start of the play, Stoppard writes, "He is not worried about the money, but he is worried about the implications; aware but not going to panic about it" (1.1).
During this first scene, Guil goes off on several monologues about what might be going on with the ridiculous coin toss. Sometimes his ideas are brilliant: "Inside where nothing shows, I am the essence of a man spinning double-headed coins, and betting against himself in private atonement for an unremembered past" (1.56). Sometimes they're more dry (especially when he tries to be logical): "Probability is a factor which operates within natural forces […] Probability is not operating as a factor […] We are now within un-, sub- or supernatural forces" (1.72). What's key is that Guil is always looking for a deep explanation to things. He may not be a particularly good one, but he is a philosopher; he wants to know why.
Guil's habit of questioning things can also be irritating. Sometimes you just want him to stop talking. You want him to just chill out and enjoy things the way that they are. This becomes especially apparent when Guil interacts with the Player. Guil sees the Player as an intellectual rival, and he constantly tries to show him up. When the Player says that he knows which way the wind is blowing (check out the "Symbols, Imagery, Allegory" section for more on wind in the play), Guil has to point out, "Operating on two levels, are we? How clever!" (2.47). Guil just has to show he knows what is going on. He's all "Hey! Look at me! I'm smart too!" It's this need of Guil's – the need to be seen as smart – that can be annoying for us as readers.
Guil's intellectual competition with the Player is most serious when they discuss death. Guil has some very set ideas about what death is. For him, death is "not anything … death is not … It's the absence of presence, nothing more … the endless time of never coming back … a gap you can't see, and when the wind blows through it, it makes no sound …" (3.343). For Guil, death is not something that can be acted. It is something that cannot be faked.
Guil's obsession with death is a bit confusing, but let's throw a couple different ideas out there. First, we remember that Guil tells the Player that "I would prefer art to mirror life, same as you" (2.324). For both Guil and the Player, art and life are very closely related. But for Guil, death is the line that separates art from reality. Art can imitate reality in all sorts of ways, but there is one thing it can't imitate: death. For Guil, who constantly seems to be looking for answers about the nature of reality, death is that thing that makes reality real. There is no death in art.
Second, we note that Guil gets the most uppity about death when he knows that he is going to die. This might suggest that Guil is not as concerned with the truth of death as he is about what is going to happen to him. That big ego of Guil's is not separate from his philosophical questioning. Is Guil constantly spouting pseudo-philosophy because he cares about truth, or because he wants to show off? Does Guil ask questions for their own sake or out of a self-centered desire to find out everything about himself (and thus make everyone else listen to what he has to say)?
We don't know about you, but if we were in prison and we had one telephone call to a friend to ask for bail, we wouldn't call Guil. Loyalty is not his forte. Upon finding out that he and Guil are taking Hamlet to his death, Ros is upset and protests that they are his friends. Guil, on the other hand, says, "Let us keep things in proportion. Assume, if you like, that they're going to kill him. Well, he is a man, he is mortal, death comes to us all, etcetera, and consequently he would have died anyway, sooner or later" (3.205). He is very good at rationalizing away his actions (or his lack of action). He's so good that we just might call him a coward.
Abandoning Hamlet is the most extreme example of inaction in the play. For Guil, there is constantly a disconnect between thinking and acting. For all of his philosophy, Guil can never decide how he will act; he can only explain how he does act. This is why the Player tells him that he needs to just "Relax. Respond. That's what people do. You can't go through life questioning your situation at every turn" (2.150). Often, Guil's philosophy can sound a lot like whining, and it's unclear what makes him think he is more entitled to whine than everyone else.
The important question here is whether or not Guil is a moral character. The way that he treats Ros and the way that he so quickly turns against Hamlet suggest that he is not. But it might be too simple to think of in terms of moral/immoral. For much of the play, the best way to describe Guil is that he is an amoral character. Since he doesn't make any choices, he doesn't have to think about whether or not they are moral. It's only where he gets pushed into a position where he has to choose whether or not to help Hamlet that his inaction is forced to take on a moral tinge.