Can you declare BS attack against someone in total cover? It's the question of the hour. RAW the answer would appear to be "no." Some argue that RAI, the answer is "yes." While I'm sympathetic to that view, up until now I haven't been convinced. However, I just had a thought which makes me think maybe the RAI answer is correct. Consider this bullet point from the Engaged State rule: "Troopers in this State can only declare CC Attack, Dodge, Idle, Reset, and Skills that specify that they can be used in Close Combat or in Engaged State." Now consider this scenario: Troopers A and R are looking at each other from 3" apart. A declares Move and moves into sil contact with R. R declares a BS Attack with his chain rifle. ... or does he? R is in the Engaged state at the time he declares his ARO. The Engaged State limits what Skills can be declared while in that state. Declaration doesn't follow the All At Once rule, only resolution does. So, RAW, it would appear that R can't shoot A. I don't think that's an intended result. I think we can probably all agree that R is supposed to be able to shoot A. While not conclusive, this suggests that the rules could mean "you may not declare Skill x except in condition y" to mean "y is a Requirement of x" that's checked at Resolution. If so, it would follow that the Total Cover rule doesn't prevent the declaration of a BS Attack. No conclusions here, just grist for the mill.
This is an interesting musing. Pages 56 and 57 of the N4 rulebook show a figure moving from total cover into silhouette contact and CC attacking, and the reacting figure responding with a BS attack. The illustrations are actually sort-of weird because it looks like the short move skill is interrupted with the BS Attack (via the illustration) before silhouette contact is made. In the next illustration it shows the figures in contact, though, and the CC and BS attacks are resolved. With this in mind... in your example above, we might actually be able to say that trooper R is not actually in the Engaged state when the ARO is declared. Trooper A has Declared that it will move into Silhouette contact, and the intended path is traced, showing that engagement will occur when the order is executed. Trooper R declares their ARO... and so-on. Essentially the movement is part of Resolution along with everything else. So R can shoot A because they are not technically in an engaged state until some point during resolution(?). But of course, if that's the case, then perhaps would R not be able to Declare a BS attack at all because of Total Cover at the point of declaration? Again common sense (and of course, the rulebook example) suggest that you can declare a BS attack in this instance. But what's the basis for that? If declared skills (including movement) happen at resolution, then it must be possible to declare a BS attack to a target in total cover, because otherwise you wouldn't be able to do something as simple as use an order to move out of cover and then do a BS Attack (note that I don't necessarily agree with this or play this way - it's just another way of looking at the same conundrom).
Answer: The part in the rules where you’re told that you specify where the attack is made from, especially when the attacker has declared a movement skill previously. Or, you know, the example in the rulebook where a trooper declares a Move around a corner and back to its original position, and then declare a BS Attack from the middle of its movement path (and receives AROs there). No one is declaring BS Attacks through total cover, they’re declaring BS Attacks with LoF to or from a moving target.
The Total Cover preventing the declaration post 1.1.1 change is an oversight. RAI is that you could just declare anything and check at resolution. Hopfully they make RAW fit it sooner rather than later. (Though it's starting to be pretty long)
Here's another reason why "may not declare" may mean "fails the Requirements check at Resolution": A is in R's back arc. A declares Move and moves into sil contact with R, remaining in the back arc. R declares BS Attack. RAW, the declaration is probably allowed. As @Lawson points out above, even though R is in the Engaged state, she can probably declare BS Attack on the basis that she wasn't in the Engaged state for part of A's movement path (otherwise we get the results from my original post which are almost certainly not intended). So CC Attack is declared, and when we check Requirements, we see from the LoF rule that R has 360 degree LoF to A while they are engaged in close combat. So the BS Attack meets its LoF Requirement, and succeeds. You would think that it would be prevented by the Engaged state, but the problem is that Engaged only limits the Skills a trooper can declare. Having validly declared BS Attack before A reached sil contact, R can now perform the BS Attack using the LoF she gains to A as a result of being in sil contact. The result is that R can shoot A in her back arc. I'm told that some metas have in fact been playing it this way post 1.1.1. I don't think it's intended. The problem (if it is a problem) is solved if "may not declare" means "fails its Requirements." In that case, "not being in sil contact" becomes a Requirement of BS Attack. So R can still declare BS Attack, but it will fail at Resolution because there is no point at which A is both (1) in R's LoF and (2) not in sil contact with R.
