I'm chiming in although I need to come back and edit more.
Rob, there is such a thing as a "proper binaural" set of microphones. I wish Len had gone a bit more in detail (about the mic design itself) as he knows more about this than my psychoacoustic former hydrophone designer self. True Binaural technique uses capsules which are pressure "omnis" ## which are aimed upward into the ear canal, typically using a dummy head, but can be used on your own head. Different from placing typical omni capsules on glasses or near your ears in that each individual's pinnae are unique including that of a dummy head. In Psychoacoustics this is known as the Head Related Transfer function (HRTF), the difference in arrival and location cues in each microphone separated by ones own head or a dummy head.
One result of this is recordings made wearing binaural mics IN the ears are OPTIMALLY played back via headphones or earbuds by the same person who wore the microphones. Playback by others, even with optimal equipment may not hear the same things the original wearer of the mics hears. Thus, the hanging omnis by glasses or clips on a hat has become de rigeur for today's field and hobby recordists in order to listen on stereo speakers or share with a wider audience.
There was a user here, moke, Mike French, who does a fair amount of Binaural recording of generally acoustic music groups using a Sennheiser dummy head. He started using the microphones aimed outward toward the stage or primary sound source as opposed to upward toward the pinnae. He calls that configuration HRTF as it relies only on the Head transfer functions and not the pinnae for accurate reproduction. His technique is top notch.
Product wise-The pinnacle of this was probably the B&K HATS (Head and Torso) heads, then Neumann made one which is a bit more modern and good looking enough to place in symphony halls etc. but each of these is upwards of 5-10 thousand dollars. Then Sennheiser made a less cost dummy head and pressure omni capsules combo in the 1,500 dollar range. Core Sound makes their three binaural offerings, each of which gets excellent reviews by their users. My old company, Sonic Research Associates, owned a JVC dummy head which I have attached a picture of as well as a stock photo of the Sennheiser mke 2002's
edit1: ## gutbucket caught my error. Here is a more pedestrian description of the differences between pressure and pressure gradient capsules:
The microphones had to be pressure-type microphones as opposed to pressure-gradient types that have directional (cardioid, hypercardioid, figure-eight, etc.) polar patterns. Pressure type mics are naturally omnidirectional and, like our eardrums, receive sound from only one side of the "diaphragm".