Top Gun the Movie is actually pretty accurate when you look at the last 30 years of "no fly zone" enforcement, which was the mission in the movie.
Many dozens of times over multiple decades in multiple theaters against multiple opponents, the vast majority of stereotypical NFZ engagements have ended in "two american planes primary and wingman have a brief dogfight against enemy aircraft to obtain ideal firing positions, involving visual identification, then end the fight with short range IR guided sidewinder missiles". There are, of course, occasional exceptions but the VAST majority of NFZ aerial combat stories look like this.
Its interesting that for 30 years NFZ ROE documents have been classified and are generally still classified and only rarely can you find an ROE illegally posted on wikileaks. HOWEVER the secret squirrel types seem to have ignored the internet and OSINT in general. So you can't legally find a piece of paper titled RoE describing how visual ID was necessary and BVR generally prohibited for all practical purposes, however, its trivial to read on wikipedia the stories of about a hundred NFZ engagements and then reverse engineer the classified ROE to match the large number of mostly identical individual engagements.
Or to summarize the above, the RoE for NFZ operations for the last 30 years remain classified, although the results of seemingly all air to air engagements have been publicly released, and traditional OSINT techniques applied to hundreds of "isolated" public anecdotes can easily reverse engineer the contents of those classified RoE documents, and the reverse engineered RoE documents pretty much mirror the fight scene at the end of the Top Gun movie; get close, dogfight into missile launch position while performing visual ID, end fight by launching short range IR missiles.