What small bird is this?

[3Gbear 3]

Hi All!  I was wondering if y'all could help me to identify the bird in these two pictures.  I took the photographs at Enchanted Rock State Park (near Fredericksburg, TX) in early July.  I believe the first picture is of a Blue-gray Gnatcatcher (0785), but I am not sure if the other one (0789) is as well. Any identification help would be greatly appreciated.

[Connor Cochrane 2,245]

1 is a blue gray gnatcatcher with the ack line over its eye. 
 

I believe number 2 is an immature Black-throated Sparrow with that long white stripe coming from behind its eye. 

[3Gbear 3]

Thank you so much for your help.

[lonestranger 607]

12 minutes ago, Connor Cochrane said:

with that long white stripe coming from behind its eye. 

I wonder if that is a piece of dead grass in front of the bird as opposed to an eye line?

 

[Connor Cochrane 2,245]

1 minute ago, lonestranger said:

I wonder if that is a piece of dead grass in front of the bird as opposed to an eye line?

 

Your right. It’s in the place where the eyeline would be. 

[Charlie Spencer 3,159]

i agree it's grass and not an eyestripe, but what does that make the bird?

[Benjamin 764]

I'm pretty certain it's still a juvenile Black-throated Sparrow, the grass is simply covering the eyeline. The gray plumage overall and lack of a strong wing pattern rules out a lot, and we can eliminate Rufous-crowned because of the streaking on the sides of the breast.

Edited July 10, 2020 by Benjamin