My daughter is an incoming freshman in engineering, so we just went through this
Your choice of engineering discipline makes absolutely no difference right now - all freshman regardless of qualifications, timing of acceptance, etc., are enrolled in general engineering. Then they go through a process called ETAM - entry into a major - where they are placed into their specific engineering types based on their freshman grades. As I understand it, a 3.75 freshman GPA guarantees you the type of engineering you want, and then from there they start going down the list and placing kids in their specified majors based in ranking until those slots start filling up.
So as far as your application goes, select an engineering first and something else second - not another type of engineering because it won't matter.
Here's the catch engineering applicants have to go through a second round of admissions review. So you'll start seeing kids getting admitted to TAMU in September in your son's second choice major, even though they are "less qualified" while you have to wait until January to hear if you got into engineering. The problem with that is by the time you find out you didn't get engineering, those other majors are pretty well filled up (depending on what you chose).
TAMU does everything they can to get you into engineering if you choose engineering as your first option - including The Engineering Academy at Blinn, Galveston, McAllen, etc. - you'll get those options over your second choice major in most cases.
In February our daughter was offered Engineering at Blinn, which is still a great option, over her second choice major (forensics), after she had friends accepted into forensics back in the fall with MUCH lower grades and scores - but it's all about timing and if you want engineering. She then got offered full admission a few weeks later, so it all worked out for her in the end, but it was a frustrating, stressful and confusing process for her.
Keep in mind, all of this is based on academic admission, not top 10% - there's a different set of rules if you're top 10%.
Hope that helps good luck!
ETA: just re-read your post and see he is top 10% so he's guaranteed admission to the university, but still has to go through engineering review. Same thing holds true here - putting engineering first and second doesn't increase his chances. He'll either be accepted into engineering or not. If he is not admitted into engineering for some reason, as an auto admit he's guaranteed a spot at the university still, as long as his second choice is still available - if not, then they will give him the option of choosing a third major based on what's available at that time.