Is there any rule of thumb concerning optimum aperture diameter as it relates to accuracy?
The only rule of thumb I can possibly think of is post sharpness. You want the post to have sharp edges. I trade off target clarity for post clarity. I wish I could both clearly, and there was a time I could, but now, I can't. So I am willing to trade off target sharpness for post sharpness.
Your eyes differ from my eyes. Your pupil diameter is different from mine. Guys whose pupils can shrink down to a pin point love bright days. Shooters with large pupils like over cast days. Since eyes are different, the aperture that works best for you will be different.
Too small a rear aperture and the target and post goes dark, so that is an obvious indication of a problem. I now have problems with the old 0.0520 and 0.0595" rear sight apertures of the M1a and Garand. I had my NM sight drilled out and I use an AR15 aperture. I use a 0.046" standing and a 0.042" all other positions. I use that same combination in my NM AR15's. I have buds who can go down to 0.036" which is too small for my eyes.
I was shooting both my Garand and AR on Saturday, and just could not get the AR to group.
An AR15 is like a snubbie. Short little sight radius. This is something that is absolutely critical to learn with an AR15:
sight alignment is more important than sight picture. I was taught this by a Marine Shooter at Camp Perry. I was struggling with the occasional wild shot and assumed that I was putting the post in the middle of my sight picture, target in the middle, and I was not. At least not always. There is an old saw, that the military used to say, that the eye naturally centers the front sight if you are using a rear aperture. This is hogwash. You have to check your sight alignment each and every shot. Alignment is critical for all rifles, but you start using an AR15, a sloppy sight picture gets magnified.
Also, stock weld on a AR15 is different. Let the charging handle touch your nose and always line up on the gun with the charging handle at the same place on your nose. I could not do that standing, but since I always put the rifle in the same spot on my shoulder, my head would go down on the same stock spot each time. But prone or sitting, use that charging handle to locate your face.