At Mazda, keyless ignition is now standard, and some vehicles have an “advanced keyless entry” system that helps alert the driver to a running engine. If the driver gets out, the doors are closed and the engine is running, six repetitions of a double beep sound inside and outside the car, and a warning light activates on the instrument panel. On other Mazda vehicles in the same circumstances, the external warning sounds only if the key fob is still in the vehicle.

And Mazda has not incorporated a system that automatically shuts off the engine after a certain time of idling.

Even when precautions are in place, some safety experts, lawyers and victims say the automakers need to do more. At Toyota, such voices came from inside the company.

According to testimony in a wrongful-death lawsuit, Toyota began an investigation into its keyless technology, conducted by its technical center in Michigan, after an employee drove 250 miles to Chicago in 2007 and realized that the remote key was still in Ann Arbor, Mich. (The witness did not know how this happened — for example, whether the fob was close enough to send a signal, but not inside the vehicle, when the car started.) Toyota engineers noted that Mazda vehicles beeped externally six times, as opposed to three external beeps in Toyota models. According to a company document cited in a deposition, they concluded that “Toyota vehicles do not have adequate smart-key-absent warning system.”

Shaun Austin, a quality control manager for Toyota in North America who testified in a wrongful-death suit, stressed the issue internally. A Toyota team in North America was in touch with corporate headquarters in Japan about adding flashing lights and a unique tone that would alert the driver if the car was still running without the key fob present, he said in a court deposition, but all those suggestions were rejected.

Contacted for this article, Mr. Austin directed questions to Toyota. When asked why the suggestions were rejected, Toyota declined to comment.

Its three external beeps satisfy the engineering society’s recommendations.

An Inquiry Without Action

At one point, the traffic safety administration appeared to start taking a keener interest in the hazards. It undertook an investigation of seven automakers in 2013-14, conducting tests and asking for documentation of their safety features for keyless vehicles. But the inquiry was quickly and inconclusively wound down.