Well, there are a few posts to answer that I am going to try to address all at once.
The first is why the 51% rule exists at all. The OP understood trying to ban in bars and was curious about how this applied to other stores. The answer was given in part (only applies for on premise consumption so liquor stores and convenience stores are okay), but let's look at it a little further. We know the rule was included for political reasons, but basically it is saying you cannot carry in bars. The problem is how to define a "bar". Yes, I know one when I see it, but the law generally has to be more specific and give us a way to identify what is a bar. So, someone came up with the concept that a restaurant will get most of its money from food, and a bar gets most of its money from booze. Most can be defined as more than half, so we get the 51% alcohol rule for bars. All it really is doing is trying to define what a bar is for us to understand.
The problem given next was how to tell if the place is properly posted. The best answer is to look at the license and see if it says "Sign = Red" or "Sign = Blue". A red sign is a 51% limit sign and a blue sign is the standard unlicensed possession sign. The bad news is that there is currently no public way to see what the actual sales are. TABC considers the sales numbers to be private information, so there is no public database to see and verify.
The next half of the problem is that the law does not say it is illegal to carry in a bar (51% place) but it is illegal to carry in a place "determined by TABC" to be 51%. So, the actual sales figures may be irrelevant and the license statement becomes the real deciding factor. TABC tries its best to keep the signs accurate in licensing, but they are dependent on the people giving them accurate figures when they apply for the license or renew it. If you really want a restaurant that is off limits to guns, tell TABC you get 49% from food and 51% from booze and they will issue the "red" type license. It can go for years with the wrong information until TABC gets enough data to verify it as wrong later.
The third point to discuss is the drinking at the hamburger stand in the convenience store. If the store has a "BF" license, then drinking on the premises is ilelgal. If they have a "BE" then they can sell for on or off premises consumption. This is not common for a convenience store, but could be what they applied for if they were smart. This means that it would be legal for them to sell from the refrigerator and let people pop one open and drink at the counter (I think, I would need to check the exact circumstances and rules more specifically).
The fourth point to discuss is what is intoxicated and how does it apply to a CHL. A CHL may not legally carry while intoxicated. Some instructors have either taught or confused their students into thinking this means no alcohol at all. This is not true. They get this because the definition of intoxication is in Chapter 49 and not in chapter 46 with weapons. And it says "in this chapter" so some people do not think it applies. BUT, the Code Construction Act (chapter 311 of the Government Code) tells us how to read laws. It says that we use the common meaning of words unless they have taken on a specific legal meaning by some definition in code or case law. In this case, I think the common meaning of intoxicated has become the legal meaning and most people only use that word in reference to the law. That way we differentiate it from the common meaning of the word drunk. And, intoxication has taken on a specific legal meaning through the definition in Chapter 49.
So, intoxication means what the law says in chapter 49, quoted in an earlier post. This clearly allows you to have a drink or two while carrying. I think this might be a bad idea, but that is my opinion. That is probably where the confused part of my earlier statement came in as instructors gave advice and students took it as rules. It also shows that a person is intoxicated if they have lost the normal use of their faculties through any subject OR if they have a .08 BAC. The important part to note is that it is illegal if you have a .08 and you are still capable of doing anything you normally can. But there really is a specific definition for intoxicated as to when you can carry, no matter if I think it is a good idea or not.
Finally, my last point was a specific one to AFCop. You got the name close enough for most people to figure out who you meant.
That is all that really counts. I stopped worrying about how my name gets spelled a long time ago (except on checks).