My 2 kroner on this one...
In a long-running role-playing campaign I was GMing, we had a standing rule allowing MechWarriors and pilots the ability to eject from any cockpit-destruction situation, but only if they made a pair of rolls first: One to notice that an incoming hit was going to be fatal, and the second to hit their emergency ejection in time. For the PCs in the campaign, this was translated into a Perception Check and a Piloting Check (with a +2 TN penalty), respectively. For NPCs, the process was basically a flat 2D6 of 8+, followed by a Piloting Skill Check with a +2 penalty.
One particular NPC, for whatever damned reason, not only suffered a disproportionate number of cockpit destructions, but also managed to pull off his last-second ejection checks every time. This character had actually reached a lance command level in the players' force, and was thus present in many officer meetings. After so many near-death incidents, I essentially ruled that he spent most of his time quietly flipping a coin with a thousand-meter stare on his face. This behavior and a basic ambivalence toward life-and-death events were maintained even when the NPC was taken over by a new player later on. This was pre-A Time of War and special pilot abilities, but the long and the short of it was that this character was effectively past fear and rage, and thus could not be intimidated, scared, or forced into retreat unless ordered to do so.
In straight tabletop play, I would likely make a character like the above immune to Antagonizer and Demoralizer SPAs, and capable of ignoring any Morale-based effects or Forced Withdrawal rules the scenario (or opposing force special command rules) might call for. In this case, the trauma made them inhumanly fearless and cavalier about danger, with no other penalties or bonuses beyond that.
If, alternatively, you wanted a character quirk that reflected enhanced fear, or which undermined their morale, I would suggest that they simply suffer increased penalties when exposed to the Antagonizer/Demoralizer SPAs, or other situations in which they may experience negative Morale-based effects. If Forced Withdrawal rules are in play as well, this character might have modified "Crippling" conditions that make it slightly more likely to trigger, such as 1 Engine hit (instead of 2), the loss of any head armor at all, internal damage in any two locations (or any one torso location), 3 or more pilot hits (rather than 4), or loses the use of all primary weapons (rather than all weapons period). Any morale penalties applied shouldn't be more than 1 point, though, to reflect what amounts to an over-cautious mindset. (Anything more severe and your warrior would likely be seen as psychologically unfit for service, rather than just "jittery.")
I wouldn't tie any traumatic effect to the presence of a single 'Mech model or weapon type on the battlefield, though. Not unless that specific warrior had been downed/nearly killed by that specific unit/weapon more than twice before.
- Herb