OP can you change this to Post-Timeskip Light (Basically Bruce replaces Near and Mello instead of L)? With L's resources, Mikami, Misa, Takaba, 2 notebooks, and his whole cult?
Ngl.
Light doesn't even last 5m in that case as Light is no longer just some kid, he's head of an agency designed to back Kira, and everything leading up to Light being made head is sus af.
Batman will instantly hack every single Kira taskforce tech, gather all files including the shit Watari deleted somehow (he's recovered lost files dozens of times before), and his first place to check will literally be Light himself in the same way Near did.
Mind you Batman has gained access to totally incomprehensible advanced alien tech in minutes, compared to having to not just learn a whole language, computer language, but even a fundamental different thought process. Batman also has hacked and has backdoors in every single government agency on the planet, he even has every single key to every nuclear armament in case of emergency (including disabling).
Light has a better chance without resources, at that point in the story he's literally zeroed in within about 5 seconds in real time.
Problem is, Light recognized he was being stalked by trained people before and has not only dealt with that but also has other countermeasurements to be showing why he ain't Kira. From what I recall, Ryuk is not screwing Light because iirc you have to specifically have touched a Death Note to see the Shinigamis, no?
Batman can sense spiritual entities. He comes into this with the ability right off the bat. Not to mention, he's dealt with this before and knows rituals and methods to see unnatural entities like the dead, psychopomps and demons anyway so... Actually tried that in one of the runs I listed above to interact with Deadman better.
And Light will never recognize he's being stalked. For example, the two situations from Death Note itself.
Batman isn't the FBI, there will quite literally be zero evidence for Light to pick up.
Batman won't miss the doorknob trick (he's literally been more anal before, not even shifting dust to reveal he's been at a crime scene or in someone's place), his cowl has x-ray so he'd see the drawer compartment, not that he wouldn't find it anyway...
Ryuk will never be able to detect Batman stalking, Batman makes no sounds, his breathing and heartbeat is nullified, even his gait has hypnosis and suggestions built in so people miss him in broad daylight, but even if he did, Ryuk being there just instantly outs Light as being Kira.
Batman omegastomps like it ain't even funny.
DCAU or year 1 Batman might be more fair but I doubt it.