The battle code is quite legacy and so is touched gingerly/rarely. That bit of code definitely predates Barca's last battle.
What you saw there was most likely related to fortifications (though could be unit settings). Roughly, fortifications encourage a unit holding on walls. The bigger the fortification level, the longer they will hold before moving out of the fortification. Settings like murderous, aggressive, normal, defensive, evasive affect it as well. Also, some more advanced marshal formations. Digging in is a primitive-form of fortification, so occurs too.
There are some checks for various units in front of them before moving forward. For them to move forward, they aren't seeing units to attack, so are moving forward to find units to attack.
So since Barca only had townsland fortifications, it had less 'wait time' before moving forward. Obviously its been too long now to know whether unit settings played a role at all.
In terms of the Taselak battle, higher fortifications, so more sitting on fortifications. Still, both the first and second battle saw units move out of fortification while others stayed because I suspect they were on aggressive unit stance, not defensive. In terms of the MI/Archers behind fortifications, if they have enemy in-range I don't think they will leave their position. Fortifications do reduce ranged damage. Compare the top section of ranged hits damage compared to the final casualties/hits at the end of the round and you'll notice them reduced due to fortifications. You'll also notice Sandalak was on skirmish settings, which reduced its own ranged casualties.
