Bobby and Zita played one game of chess: his new variation, called Fischer Random. She claims that she won and then became frightened. Perhaps he'd become violent toward her, she thought, because she was a woman and, also, not yet even a master. (p.237)
As far as I know, this is the earliest mention of Fischer Random, predating a passing reference by Fischer at the press conference opening the match with Spassky, September 1992. After the match Fischer stayed in 'Magyarkanizsa, in the northernmost reaches of Serbia, on the border of Hungary'. There he made the acquaintance of the Polgar family and, with their encouragement, later moved to Budapest.
All of the [Polgar] sisters played chess with him, but acceding to his preference, they played Fischer Random. Invented by Bobby, this was a variation on the standard game. [brief description of rules & reasons for playing] As it happened, 18-year-old Sofia, the middle of the Polgar daughters, beat Bobby three straight. Zsuzsa [Susan] played him "countless games" and never revealed the results other than to say she did "all right". (p.260)
For another account of this, see my post Pictures of a Fischer Random Precursor. Brady relates another anecdote involving the Polgars that was new to me.
[Fischer] became angry, when Laszlo [Polgar] showed him a book published in 1910 by the Croatian writer Izidor Gross. The book described a variation of chess that seemed to be the forerunner of Fischer Random, with the exact same rules. Muttering something about Gross being Jewish, Bobby went on to change the rules of his variation to make it different from Gross's. (p.261)
While in Budapest, Fischer also made the acquaintance of Andrei [Andor, Andre] Lilienthal, who arranged a meeting with FIDE President Kirsan Ilyumzhinov.
Bobby showed Ilyumzhinov how Fischer Random was played. [...] Ilyumzhinov also offered to put up millions for another Fischer - Spassky match, but all Bobby would say was "I am only interested in Fischer Random". (p.264)
It's not clear from Brady's account when this meeting took place, but the February 1996 issue of Europe Echecs (p.22) gives a date of 15 December 1995. That would have been less than a month after Ilyumzhinov was first elected FIDE president in a special election. Fischer's official announcement of his variant only merits passing mention.
Bobby felt safe enough to travel and eventually went to many countries [...] to Argentina to promote his Fischer Random variation (p.268)
I posted about that June 1996 event in Fischer Announces Fischerandom. The last two references by Brady, from Fischer's final years in Iceland, are more difficult to date.
Bobby couldn't escape chess, although he desperately wanted to. "I hate the old chess and the old chess scene", he wrote to a friend, making reference to his invention of Fischer Random. Nevertheless, there were entrepreneurs flying to Iceland [...] who were trying to entice him to play -- any kind of chess was acceptable, just to encourage him and ease him back into the game. [...] Another match against Spassky was discussed (and Spassky was agreeable to playing Fischer Random), but these talks ended in a matter of days. (p.306)
Despite his promotion of Fischer Random and his rejection of and scorn for the "old chess", he still played over games, tempted by the action of contemporary tournaments and matches. [...] He never wavered from claiming that all of the games in the 1985 [Karpov - Kasparov] match were fixed and prearranged move-by-move. [...] Others held that his accusations were a ploy to promote his new Fischer Random chess. (p.309)
I'm a member of that 'others held' camp -- see Fischer: 'The *Old* Chess Is Dead' -- but I wouldn't call it a 'ploy'. He sincerely believed that his variant would save chess from 'very interesting, beautiful pre-arranged games being created by very intelligent players, working with computers'.