The question of whether or not a twist may take place before designating with TAG was already
asked and answered, and thus became eratta. The answer, according to the Rules as Written, is
no.
Said ruling would also apply to the question of twisting a turret (such as on a tank, or a VTOL's chin-turret).
Here is the reasoning, following the rules as written:
Total Warfare, p. 37; Weapon Attack Phase
... The player controlling the firing unit
declares whether it will twist its torso or flip its arms or turn its
turret, and in which direction. ...
... The player controlling the firing unit declares any
torso or turret twists and attacks he plans to make using that
unit’s weapons, as described above. ...
Total Warfare, p. 37; Torso/Turret Twist
Torso or turret twists are made when declaring a weapon attack, but the torso or turret remains pointed in the same direction throughout the remainder of the turn. This affects physical attack firing arcs as well; the torso or turret returns to its forward-facing position during the End Phase (see below).
Meanwhile, TAG specifies
Total Warfare, p. 142; TAG (TARGETING ACQUISITION GEAR)
Instead of making a to-hit roll for TAG during the Weapon Attack Phase, all units needing to make TAG to-hit rolls do so after the end of the Movement Phase (Aerospace), but before the beginning of the Weapon Attack Phase (initiative is still followed, however).
It is pretty inarguable that according to the rules as written, a 'Mech with a torso-twist, or a vehicle with a twisting turret,
can not make that twist between the movement and shooting phases (MegaMek implements this as happening during the off-board artillery phase, for what that's worth.)
This is an appeal to have the rules changed. Firstly, here is how I would change the rules:
Simply state that a unit may make an appropriate twist as-necessary to bring a target to bear when employing TAG,
however this locks the twist to that direction until the beginning of the next turn. For example, a 'Mech could twist its torso to the right in order to employ a head-mounted TAG to target a unit in that arc, but that locks the 'Mech's torsto-twist to the right for the duration of its firing phase.
Alternatively, though it would be more complicated, one could state that all TAGs which are going to be used are used in the firing phase before all weapons - the firing phase begins, all TAG-equipped units may twist and make their TAG rolls first, and then other weapons begin firing, with the results of TAG locks resolved.
(I would also expand this ruling to state that, should it come up, a 'Mech may flip its arms to employ an arm-mounted TAG, but that also locks the arm-flip condition.)
Here is my reasoning: the rules-as-written ruling almost certainly came as a surprise to many players who undoubtedly considered it an 'of course' matter that you could twist a torso to designate TAG; informally, most players who meet up in non-tournament conditions to play over a physical tabletop probably don't even know about the TAG-twist ruling, and are already assuming that one can simply twist to TAG and then that thereafter locks the torso twist.
Additionally, this ruling greatly reduces the utility of many 'Mechs, canon and custom-designed, which quite naturally decided the HD slot on a BattleMech, or the turret on a tank or other combat vehicle, was the natural place to put TAG, not realizing that it would be fixed-forward anytime they wished to employ it. A non-exhaustive list of units with TAGs in the HD or another torso location, or in the turret is:
Black Watch BKW-9R,
SturmFeur Heavy Tank Steiner,
Perseus P1P,
Moltke MBT M3,
Black Hawk-KU BHKU-OG,
Men Shen MS1-OA and -OF,
Tessen TSN-1C, -C3, -1Cr,
Maxim (I) Heavy Hover Transport Company Command and Standard,
Komodo KIM-2, and -2A,
Sha Yu SYU-2B,
Zephyr Hovertank C3i, Standard, and Royal.
Meanwhile, some vehicles do have the TAG mounted in the front. Given that, it seems that having a TAG mounted in the front of a vehicle is supposed to be a limitation compared to having it in the turret; and a great many 'Mechs mount TAG in the head, where it seems so natural to mount a sensor, whereas I was unable in my admittedly quick search, to find a
single 'Mech with TAG mounted in an arm location, where it would have the greatest actual utility following this ruling. There are, however, 'Mechs with their TAGs mounted in the legs
(?!), where they would both be unable to make use of any twisting, and must be used from height 1 - obviously a limitation compared to being able to twist-and-TAG.
Furthermore, this leads to the 'optimal' TAG-equipped unit being a combat vehicle with two TAG units, one on each side, sponson-mounted so the vehicle can always bring at least one TAG unit to bear against any target it wishes to paint; a configuration that precisely zero (0) units I was able to locate possesses. In fact, I could not locate any unit, at all, possessing more than one TAG.
The Rules as Written ruling prohibiting twist-to-TAG appears to be not in keeping with the actual intent behind the way combat vehicles and 'Mechs were put together. It exists to the detriment of anyone who wishes to employ 'scout-spotter' units in their gameplay by forcing them to awkwardly face only the front of their units at whomever they wish to TAG-designate, and quite frankly it fails to pass the sniff test - it just frankly seems like an absolute violation of common sense.