Performed by two actors over two acts, Pantomime opens with Harry Trewe, a retired English actor in his forties who now runs Castaways Guest House in Tobago, reciting lines from a pantomime adaptation of Robinson Crusoe he once coauthored. Harry's employee, Jackson Phillip, a retired Trinidadian calypso singer, tries to serve him breakfast while Harry pitches Jackson on the idea of performing the pantomime together. Jackson reminds Harry that instead of rehearsing the play, he should focus on renovating the hotel first, as the facilities are run down.
Harry reveals that he has been up all night trying to find out how his guests could be entertained as promised in the ads. Jackson insists he has left performing in the past; he moved to Tobago for peace and quiet. He does not want to play a role in the production, particularly if he is expected to play Friday, the cannibal-turned-servant in the original Robinson Crusoe. In an attempt to create a light, satirical piece, Harry then suggests reversing the roles, with Jackson playing the part of Crusoe and Harry playing a white version of Friday. He even takes off his clothes to get into the role of Friday, but Jackson urges him to remember his manners, even if there are no guests around yet.
Eventually, Jackson goes along with Harry and begins improvising the race-reversed pantomime. In a sarcastic critique of imperialism, Jackson portrays Robinson Crusoe as a violent man who forces his language and beliefs onto Friday, played by Harry. He also points out that immigrants from the colonies are now frightening the British. When he improvises a calypso song, Harry sees the potential of it and wants to capture it with a tape recorder. Jackson, however, takes this opportunity to force his ideas for the play onto Harry. He makes Harry play a seagull, which Harry finds humiliating. Jackson ignores Harry's demands that he stop the improvisation. Jackson explicitly compares their play with the history of imperialism and refuses to commit only partly, drawing a parallel with the British's treatment of the people in the Caribbean and Harry's domineering attitude. At the end of Act One, Jackson pouts about Harry not showing him more respect. He goes back to fixing a table, not wanting Harry to interrupt or help him.
Act Two opens with Jackson making excessive noise while fixing the sundeck. Even though Harry is annoyed by Jackson's "vindictive" hammering, he apologizes for having hurt his feelings earlier. He blames his ideas on the heat and loneliness; Jackson suggests going back to England if Harry finds Tobago boring. Harry says that all his savings are tied up in the hotel, and that he came to Tobago to forget his wife and son. Jackson suggests that Harry's issue is loneliness, and asks if he hasn't gotten over his son's death yet. Harry evades the question by getting Jackson to recite a serious-toned monologue written from Crusoe's perspective. The poetic monologue references Harry's own loneliness and grief. Jackson criticizes the interpretation, saying that Crusoe had a faith that Harry lacks. Jackson also reminds Harry that instead of thinking about his wife and son, Crusoe's first thoughts would probably be about killing a goat for food and clothes.
When Jackson asks for a five-minute bathroom break, Harry tells him to use his private bathroom instead of the dirty staff toilet, to save time. Jackson declines the offer, indicating that he would not feel comfortable using Harry's toilet because they have not attained true equality. He compares their situation to the tendency of the British to grant independence to colonies too quickly, leaving political, social, and economic turmoil behind.
Frustrated with Jackson, and having been drinking Scotch all afternoon, Harry hides under the table with an icepick. Upon returning from the bathroom, Jackson perceives danger, and retreats. He comes back having killed the hotel's parrot, which he tosses to Harry. The tension subsides as the men have another drink. Harry toasts to his ex-wife, Ellen, which Jackson feels is inappropriate because she is not with them. Jackson leaves and returns with a photo of Ellen. Using it as a mask, Jackson forces Harry to confront his past and all the negative feelings about his wife, who killed their son in a drunk-driving accident. He is also envious of his wife's success as an actress. Harry reveals that he wanted to play Robinson Crusoe because, the first time he performed it, Ellen played Crusoe and Harry played Friday in greasepaint blackface.
After he has poured his heart out, Harry weeps openly. However, the confession has been beneficial to Harry, who has calmed considerably and quickly goes back to dismissing his grief as insignificant. Jackson brings attention to Harry's continued denial, telling him he is making "a mole hill out of a mountain." The play ends with Jackson telling Harry that he is willing to retire as a factotum and become a performer again, and he sings his earlier calypso about them putting on Robinson Crusoe. However, Jackson tacks on the condition that he would like a raise.