Is this the type of light...?

[Alistair]

I'm not lookin' for C&C, for I know these are just snapshots (My boy just got back from being with Granny for a month & I have my daddy goggles on!) that I took for other family members for on FB. I was just wondering, as the title states, is this the type of lighting in the eyes that is desired in portrait shots?

 

[Big Mike]

It's better than nothing, but I'd say that it's far from what I'd like to see in a nice portrait.

When I think 'nice portrait', I think about good lighting....and good lighting will often result in nice catch lights in the eyes.

It's not a rule, but 'soft' light is often preferred for portraits...and a large light source is the key to soft light. Therefore, soft light will likely produce large catch lights in the subject's eyes.
In a studio situation, you might be able to tell the size, shape and position of the light, just by the catch light in the eyes.
Outdoors, you may have a much larger light source (the sky, or something large & bright like a building in the sunlight)...so even more of the subject's eyes my be lit up with that reflection.

On the other end of the spectrum...we have small 'hard' lights (like a unit or built-in flash). These usually ensure that you do have some light reflected in the eyes, but since they are relatively small, the reflection is small as well. Like I said, tiny catch lights are better than none at all...especially when the eyes aren't getting enough light.

In your examples, the eyes are quite dark so it's good that they do have at least a tiny catch light...but it would be much preferred, if they weren't so dark in the first place. (not meaning his eye color, but the lighting in the room etc.)