This is a great idea..
I have been thinking bout this all day since I saw it posted this morning.
An illuminated sound level meter (the LED type rather than a moving needle) would be much more practical in a dark room and would be viewable by all nearby. Would even be seen in any video footage if it was in front of a camera.
This method will take a bit of trial and practice to see if it works out.. Not all EVP's are quiet.. so you should be able to see results quite soon. Just because we don't hear it does not mean that a sound level meter wont.
Another thing we have to consider is frequencies. EVP's might be coming through on something other than just normal sound waves.. this could explain why we don't always hear them but electronic gear does.
As a further extension of this type of device, you could have a set of IR soundlevel lights sat in front of any locked off night cams..
This would help to do a few things.. It would show if anyone approaches the cam from behind in order to manipulate the evidence.. they would not see the sound level lights flashing but the cam would and footsteps would appear obvious.
The IR lights would also not scare off anything nearby and would maintain total darkness. They will act as good visual marker for locked off EVP work in the same location.