I don't think the problem changes. The issue is not that the target only has the same time to react as it does now (because fire control isn't currently detectable). The issue is that if fire control becomes detectable by the target only, rather than generally, then there is an advantage in micromanaging the attack so you don't illuminate your target until the last second, because if you use fire controls as normal the target knows it is the only possible target and gets a warning that it doesn't get now. That advantage gained through micromanagement doesn't exist under the current game mechanics and it wouldn't exist if fire control were generally detectable because just like now with active sensors no one would know who you were shooting at, if at all. The micromanagement advantage only exists if fire control is detectable solely by the target.
I'm actually trying to say something else - sorry if I'm not being clear. My observation is that if you made fire control illumination (as opposed to specifying a target) detectable, it would be consistent, given the current target switching abilities, to only have the fire control actually illuminate the target for the last 5 seconds (let me put off the realism of this 'til a later paragraph). This is based on the fact that I can aim my missiles at one ship and then switch targets at the last instant; this is mechanically the same as (the ship's fire control suite, by which I include onboard computers, datalink, active tracking etc.) guiding them to waypoints through datalink right up until the last 5 seconds, and only then illuminating the target. In other words, no micromanagement would be needed, because it can be assumed that the ship's fire control suite will always be doing the micromanagement, and the result is that targets are only ever illuminated for the last 5 seconds (unless they're manually illuminated for another reason such as intel gathering or as a pointed message).
Now for realism: I suspect you'll object (and I agree with the objection) that only requiring illumination for the last 5 seconds is a bit unrealistic
IIRC, the reason for Aurora fire control radar is that an active contact actually has an "uncertainty blob"; it's location isn't actually well enough determined to guide a missile properly. It seems like this blob should be proportional to the distance to the target, so that e.g. you have to start illuminating the target when the missile is 90% of the way there, because that's the point where it becomes too late to correct for the uncertainty. I've come up with two ways to manage this based on whether a short or long period of illumination is required.
Short illumination: Have a "terminal guidance time" tech that tells how long (e.g. 30 seconds) a target needs to be illuminated before a missile can hit. The problem with this one comes up for AMM - the entire flight time of the attacking missiles through the detection envelope might be shorter than this time. In addition, from a practical point of view there's not a lot of additional benefit to knowing that missiles are coming in 30 seconds before they hit, i.e. it's not worth screwing around with coding up illumination detection.
Long illumination: Have the requirement for illumination be a percentage of the total flight time/distance, i.e. illumination turns on when missiles are 90% of the way there. The problem with this one is figuring out what "90% of the way there" means, since this will change depending on whether the target is coming towards you or away. Another problem is that target switching would be way too slow - you shouldn't need to illuminate for an additional 1/2 hour in order to correct a missile from one ship to another ship in the same fleet - and trying to solve this problem opens one up to micromanagement exploits. I've got a mechanism that I think has a chance of working - let me know if you want me to post it.
To phrase things a different way, I think there's two things going on:
1) From a realism point of view, targets shouldn't have to be illuminated for the entire time of flight of a missile - it's only at the end that precise location information is required.
2) Trying to make the terminal guidance phase (when illumination is required) long enough for the target to take significant action (i.e. longer than a minute or two) is a yukky problem, and can lead to the sorts of micromanagement exploits that you're worried about.
John