Enter John of Gaunt, sick, with the Duke of York [and attendants]
GAUNT Will the King come that I may breathe my last
In wholesome counsel to his unstaid youth?
YORK Vex not yourself nor strive not with your breath,
For all in vain comes counsel to his ear. (2.1.1-4)
A quick segue: we’ve just been told that Gaunt is sick, dying, and wanting to see King Richard, and here he is; the two scenes more or less overlap. This too is a private scene, which begins as a conversation between brothers, a conversation which they both know to be their last. What does it mean, to Enter … sick? Gaunt could enter walking, the state of his health suggested by his gait (a stick? halting? leaning on York’s arm?) and costume (an informal gown, probably furred, perhaps even over a nightshirt, and probably a linen coif, a close-fitting linen cap, perhaps with strings hanging down, which tended to suggest age and infirmity; an embroidered linen night cap is another possibility, but it was fashionable and connoted informality and domesticity, rather than being simply what was worn in bed, or by an old man). There’s enough time for a costume change, and covering such a change might be one of the functions of the previous short scene. I think it’s likely that Gaunt is carried in, in a chair or litter (a modern dress production might use a wheelchair). There needs to be a contrast with his doughty vitality in earlier scenes (even though he’s repeatedly characterized as old Gaunt, he still has much to say and plenty of energy), and immobilizing him in a chair would have that effect, especially with a rug over his legs. A bed would be unnecessarily complicated, and also hamper the delivery of his long speeches in the scene. The attendants are thus an editorial addition, needed to carry or push a chair.
Gaunt wants to use his last breaths, speak his last words, to give advice to his nephew the King. He is a father-figure here, the absence of his son Bolingbroke still fresh in the minds of the audience, and the King is now the wayward son, unstaid, unsteady, out of control. Historically, Richard was in his 30s by the time of Gaunt’s death (and Gaunt was in his late 50s), but Shakespeare’s Richard is written as a youthful, even childlike figure. Wholesome is interesting, because it is being opposed to Gaunt’s unhealthy body: his words will be strong, whole, even though his body is failing (whole, hale, health; health and wealth; hale and hearty; heal and weal, a tangled cluster of etymologically cognate terms). Great-uncle York is skeptical: there’s no point in trying to give advice to the King; all in vain comes counsel to his ear, there’s no point, he won’t listen to anyone. Don’t vex yourself, get wrought up, and waste your (failing) breath on him, he says to his brother.