That's what I meant by saying that The Joker can be truly unpredictable and impossible to pin down to one specific MO, or one specific method or style of killing. Maybe one day he kills 2 people, the next 1 person, and the new a dozen.
As for comparing to real life killers, it can definitely be useful to look at this through that lens, because that's exactly what Reeves has done with The Riddler. For Riddler, they clearly drew major inspiration from Zodiac among others. Zodiac was a very specific kind of killer. Zodiac killed several people, had a slight flair for the theatrical (wore a mask once like this Riddler does), and toyed with police extensively. He sent ranting letters, drawings, and puzzles (which were nearly impossible to solve) to police on numerous occasions. His true motivations were ultimately unclear, although his letters gave some clues. He enjoyed some attention from police and the media with his letters and puzzles, but never was brazen enough to show his face or reveal his actual identity. He was smart and cunning enough to evade capture and his still never been truly identified to this day.
Zodiac was a good (but not perfect) analog to a character like The Riddler, which Reeves was smart enough to consider. Reeves took the concept and aesthetic of Zodiac, then applied it to the Riddler and adapted/amplified these aspects to fit the world of Gotham and Batman. He gave him a specific motivation and specific targets (high ranking officials/politicians), made his murders/crimes/riddles more grotesque and over-the-top (Zodiac mostly just shot people), and has obviously given him a major over-arching plan for Batman and Gotham, rather than just making him a simple murders who kills a few random people.
Whichever direction he decides to go, it's likely that Reeves would do something similar with a character like The Joker. Draw inspiration from multiple serial killers, mass murderers, and/or gansters to come up with his own cinematic version of The Joker that will fit the world and universe he has established, obviously adding theatrics and comic book flair. But Reeves keeps harping on how realistic and "grounded" he wants his Batman to be, so there will naturally be some elements of realism applied to his Joker, as well.