I think just based on basic profiling, he'd narrow it down to males above a certain age. Kira still wants to hide out in Morioh, so it's only a matter of time before he finds someone that matches.
Only issue is the same thing that L ran into with his own Kira - actually pinning it on the person with evidence. For the most part, Yoshikage Kira's still pretty careful and inherently doesn't leave much evidence behind. As mentioned above, the Morioh Gang only stumbled upon him by chance because of the whole "stand users are drawn to one another thing." Kira's also really impulsive, so I don't think the whole "actually, I'm L" thing would work in a public. He might just get dusted because his ego got bruised at being suspected. But he's also dealt with serial killers before, so maybe he wouldn't even bother confirming in person.