Okay, first off I was wrong about the cohesion. I looked at the side-bar for cohesion and it was one iteration lower for Holmes than for the other 2 division in the corp. After looking at the actual cohesion level there was little difference.
Still I wanted to have a controlled environment to test with defined starting parameters so I built my own scenario. I used Bragg(Dispirited Leader), Hood(Strong Morale) and Forest(neutral) each with an identical division which they already commanded at scenario start, each with their own supply train. I picked these leaders because they have high strategic ratings and I didn't want any of them to go passive during the middle of testing. I used Longstreet** and Wheeler** for stack commanders. They were easy to choose because they are neutral to cohesion at their ** ranks and I wanted to be certain that there was no chance of Bragg or Hood not wanting to follow an equally ranked commander even if the tested generals had a lower seniority than a 1star commanders; safe is safe. (1) I also used 3x 3/1/1 brigadiers with no characteristics and very low seniority as assistants to Bragg, Hood and Forest so that there divisions would not be under-commanded. All the units started the scenario in Springfield LA sitting on a depot with 2000/2000 so that they wouldn't be under-supplied at the get-go.
I tested by running the 3 division from Springfield LA up to Corinth TN at normal marching rate with the RoE on defensive, checking their cohesion during the turns and then their recovery after their arrival in Corinth.
The first thing I learned, by taking Bragg outside of the stack his division's upper cohesion limit immediately drops by 5. Put him back in and to goes to normal again. Note, just as it is stated in the description of the Ability, only the limit drops, so if the division's average cohesion is 80(scenario start) and it is at the upper limit and the limit drops to 75 by taking it outside of the stack, its actual cohesion still stays at 80; it displays 80/75. It's just that if it drops below 75 it will not go back up higher than 75.
The 25% lower cohesion recovery rate played less of a role than I thought it would. Mathematically it looks like it would make a big difference; in the game it made little difference. Maybe this is not working. The recovery rate that you see in the tool-tip was the same in all division almost all the time. One exception was with Forest(?), but more to that later.
I also tested out the opposite of Dispirited Leader, which is Strong Morale, which gives a +5 Cohesion bonus to units under this commander. I used Hood* to test this, as a lone commander and in a stack with a higher ranking commander. The limit did not go up at all when outside of a stack commanded by the higher ranking general**. It also did not go down when put into the stack. In fact Hood's division's cohesion upper limit was the same as Forest's division's(!!). Why I don't know. What the +5 Cohesion bonus would be other than raising the cohesion limit by 5 I couldn't discover; but it's not the limit that is affected. So where the bonus plays a role I don't know. Maybe it is only reflected during combat and in every-day-life(marching, weather, etc.) it plays no role.
One other odd thing that I observed, which had nothing to do with all of this, was that every time I started the division marching up to Corinth, Forest was soon falling behind and sometimes by the time they all had reached Corinth Hood was falling behind Bragg too. After a couple of times of seeing this I checked the seniority of Bragg, Hood and Forest. They are in that order and it looks like the seniority determined their marching order. And since they were all taking the same path it appears that marching in different stacks along the same roads, being behind gives you some disadvantage. Forest always started loosing more cohesion than Bragg and Hood. And by the time Bragg and Hood were at Corinth, Hood's cohesion was slightly lower than Bragg's. It was like this every time. So one time I gave Forest his marching orders first and sure enough, after the first turn, he was right up there with Bragg and Hood and they all had almost identical cohesion, but if I just let the turns run--I had given the move-orders for the entire march on the first day by just dragging the stacks from Springfield to Corinth and dropping them--without interfering, Bragg was soon out in front again. Little trivialities that you learn along the way
I only ran the test once with the 2star generals as commanders, but for what ever reason, all three divisions reached Corinth on the exact same day, which never happened with the divisions marching alone, as if Longstreet and Wheeler, being of higher rank were able to cooperate better and keep the march moving without that the divisions were bothering each other. They also arrived with less cohesion loss.
I've attached all the modded files if you want to look at this yourself. I'm not attaching any saved games because you'd have to look at all of the turns of all of the saved games to get an overview and you'd be just as quick running the tests yourself. The only thing I might have changed on this scenario would be making Corinth CSA owned from the start as it causes the divisions to go to offensive RoE when entering the region.
(1) I wanted to use John H. Morgan too as a third stack commander, but he only has one model, I assume because his characteristics do not change when being promoted from brigadier to major-general and I could not find out in the forum how to build him into the test scenario as a maj.gen. If you have a simple solution for doing this I'd sure like to know it for the next time I have to do something like this.
Edit: PS the orange wedge?
. So let's play AACW Trivial Pursuit 
, the Gifted Commander, Good Commander and Strategist abilities reference the 'ability level' of the commander. From what I've been able to find out, the ability level is another characteristic just like the Strategic/Offensive/Defensive ratings and can climb just as these can, and it appears that the ability level only affects these abilities and no others, so in other than just a hand full of generals it will play absolutely no role. The question is, where and how can you see the ability level ob a general, and does it really only affect those three abilities?
