12 fpe at the muzzle is all you for gray squirrels to 50 yards. I don't take shots past that in the woods regardless of energy. I'm just not accurate enough to take humane shots at little critters past 50 yards unless I'm on a bench. Deer is a different story. They're a much larger target area. It's a pie plate compared to a nickel.
While it’s not my preferred approach, here’s a quick scope cam clip of anchoring a gray squirrel with under 5fpe terminal energy.
Ah I see now, not just chest shots but also in .22 cal. For a round nose pellet to hide and soft tissue of a gray squirrel, I have no doubt 500fps at impact would penetrate sufficiently, but like you already acknowledged, placement would have to be perfect and avoid bone.
The first squirrel I shot with an air rifle was with my 1377 pumped up 7 times for about 500 fps and about 4.2 fpe. It was only 10 yards or a bit less away. I hit the shoulder. I found the squirrel several days later. It had died, apparently from an infection or something. The pellet did not make it through the shoulder. It broke the shoulder so the squirrel could not climb. I have not shot at another squirrel with that gun and will not. I think it probably would have killed it quickly if I had hit the ribs or the head but hitting the shoulder is something that will happen sometimes. Wounding an animal like that is not something I want to repeat. Even a squirrel deserves a quick death.