Some more thoughts on this...
In the ASLRB most, but not all, rules where you must do something include the word "must". Most, but no all, rules where you have a choice include the word "may".
In C6.5 we have two portions of the rule that work with each other.
- "... it may place a ½" -1 Acquired counter on its target ..."
- "The target remains acquired until ..." and a list of actions that cause loss of acquisition.
Note that you have a choice to place an Acq, but if you do place that acq, you can no longer directly choose to remove it, it is lost indirectly due to other actions, some which you obviously can choose to do (like move). I would suggest that the Acq "
must" remain on the target (with an exception) until one of the listed actions takes place. the reason I believe it does not actually say "must" is due to C6.51.
- "He may choose which of his previously acquired targets will remain acquired, but need not specify which one until he fires at it or that unit has finished its MPh/APh/RtPh/CCPh-Withdrawal (whichever occurs first)."
- "If an acquired target leaves its present Location and thereby goes out of the firer's LOS (as per 6.15; a free LOS check may be made to ascertain if this occurred), the ½" Acquired counter remains in the last Location that target occupied prior to leaving the acquirer's LOS."
The first statement allows the defender a choice, although it is limited. The second statement gives direction regarding where said Acq would be placed given the loss of LOS condition, however, it also does not distinguish between players regarding the free LOS check. I would suggest that LOS check is free for either side. The timing of the final placement of the Acq is controlled by the firer to some extent, and could potentially use this choice to their advantage, i.e., a multi-unit stack splits up, you don't move the Acq with the first unit, and if it clearly goes out of your LOS (no free LOS check if you have not declared you are tracking said unit), the Acq still has the remaining units as potential targets. The risk is that a unit actually does leave your LOS, you did not check it, and you declare a shot further along when it is clearly in LOS, and your opponent challenges the acq placement and it is determined you lost LOS and the acq is no longer in play for you. This is moot if the stack is a single unit. Either you lost LOS (and the Acq is appropriately place, or you don't, and it ends up with the unit, and the Acq "must" follow the target regardless of when the firer actually moves the Acq counter. Either side could potentially use a free LOS check in every Location moved through to determine if LOS was lost.
The mechanics of this are not stipulated in detail and I suspect everyone has a preferred method of manipulating the counters during movement.
In
@EJ1 's first example, the stack is a single unit and per C6.5 it must be tracked until loss of Acq conditions are met, so the firer really has no other choice other than move the Acq counter with it, although the timing of that is clearly a choice. I would also suggest that given the tight LOS, it would be prudent for both players to determine the legality of placing the Acq in the new, potentially out of LOS Location prior to any shot being declared/taken, and I have to believe any defender would take the LOS check prior to declaring any shot.
In
@EJ1 's second example (with the moving vehicle as the firer) I would suggest the defender could either 1) remove/set-aside the Acq on his unit when the attacker leaves its current Location, or 2) remind the attacker to remove his Acq. And yes, mistakes can occur (how many times do you mistakenly unconceal some of your units) and you may get some intel prior to the Acq getting removed. If that intel (or lack thereof) is important to you I would suggest a reminder regarding loss of Acq prior to MPh if there are any Guns with Acq associated with units that can still move.
When we play, we normally leave the Acq counter behind when we move. At a minimum that marks the starting location of the moving unit (although now with Movement Trails it is not as big a deal). In addition, it makes it easier to deal with moving the unit as it is not encumbered with the additional counter.
Lastly, I am almost positive (99.9%) that the acq line is controlled by each player. You have to select one of the linked counters for it to show, and unit selection is per player.