Another motivation could be to help a friend. Suppose there is a female friend in the story who is in trouble and needs a female - looking ally. Brian, being the selfless and brave character he is, might decide to crossdress to be that ally. This would not only show his loyalty but also his willingness to go to great lengths for those he cares about. It could also add a touch of heartwarming moments to the otherwise action - filled fanfic.
Maybe it's a dare or a bet among the crew. In the 'Fast and the Furious' world, the characters are always up for a challenge. If someone in the crew dares Brian to crossdress for a day or for a specific event, his competitive nature might drive him to accept. And this could lead to a series of hilarious and interesting events as he tries to go about his normal life while crossdressed.
One possible motivation could be a undercover mission. Brian is often involved in dangerous and tricky situations in the 'Fast and the Furious' series. Crossdressing could be a perfect disguise to get close to a target. For example, if the target is a very cautious person who only trusts women around them, Brian could crossdress to gain their trust.