I.v. Swearing Oaths - BBC '80

Jacobi's Hamlet puts that "antic disposition" on very early in the play, and one could easily say that this is a mad Hamlet, not a pretending Hamlet. However, Hamlet is self-aware enough to know that he is touched with insanity (or has consciously given in to it in order to rebuild himself for his mission), so he can say he'll act mad, knowing full well he IS mad. Characters who lie to each other breed ambiguity.

The sequence starts with Hamlet's "Hillo, ho, ho, boy! come, bird, come" played as an actual bird call, immediately setting the tone for the "wild and whirling" nature of his discourse through the rest of the scene. As usual for Jacobi, the character is mercurial and can change tone on a dime, making something different of each line. Though mostly manic through the scene, he comes close to tears when he invokes his "businesses and desires". His grief comes in waves (as I can confirm such things do), usually upon any reminder of his father's death. The Ghost's voice coming from the earth is another such moment. Though the words are mocking ("old mole", "truepenny", and all that), Hamlet is on the verge of breaking down while uttering them. This Hamlet has adopted a "mad speech", but some of his emotions cannot be hidden.

Though he seems lost in his own world, Hamlet shows he is nonetheless alert when he overhears Horatio's "This is wondrous strange" from afar. He says "in your philosophy" in this version, but there's enough tenderness between the two of them that we don't necessarily feel that Hamlet is ostracizing Horatio. Instead, the old school friend seems to be the only person Hamlet is close to (he makes an effort to include Marcellus in "scholars and soldiers", so Horation must already be included). Horatio is so astonished by his friend's turn that he may feel like a complete outsider. He is indeed a stranger to this, where Hamlet is not, and so there is a divide between the characters, though not one Hamlet consciously creates. There is a certain obliviousness to Hamlet in Jacobi's performance that makes us believe he really has gone crazy.
In the Act's final moments, Jacobi throws in an unscripted moment to motivate the "let's go together" repetition. After his rhyming couplet, and as the other men are walking away from him, they stop and look back, as if doubting his sanity. Hamlet looks to them then makes like he sees the Ghost again. They look in that direction and there is nothing, and Hamlet giggles wickedly at them, like a child who has just pranked his friends. "Nay" here becomes a "no, no, I'm just joking". He has shown them what he means by putting an antic disposition on, but has he convinced them that it IS a put-on? This Hamlet is so wild that Horatio and Marcellus may be more motivated by fear than trust.