Can I use my gun stat? / Combat characters in talky encounters

Being an internationally renowned role-play guru, I am often approached by apostles wishing to bathe in the waters of the well of my RPG wisdom.

Or something

I received this email earlier today:

What do you do when you have a good group of characters that work well together and have a varied mix of skills that they keep using .. but there's one who is usually left out for example : an ex military PTSD Sufferer who is now something of a Conspiracy theorist .. skills wise has a few bits all over The game I'm running is not generally combat led but there is inevitably conflict each week.. in this he takes part .. pulled out a fire extinguisher and started blinding the zombies this week which was cool ..

But I don't get how to get him more involved in the social / mental side of things without leading him by the nose and railroading the adventure
I want them to make their own choices and then if there' consequences .. gotta live with it .. have you any insights ?

My considered reply was:

Tough one. Maybe ask him straight out, how can I get your character more involved in the thinky/talky stuff? That way he feels as though he has input, and that his input matters.
Be sure to tell him that his character kicks add in fights, though, and keep saying its the character, not the player, that you're struggling to engage.

You could ask the other players if they have any ideas how you or they can get the character involved.

You could stage some encounters that focus specifically on the character, maybe triggering a combat flashback or reminding him of a past combat encounter that traumatised him in the first place. He could then roleplay out his characters reactions and fears with the other players or some NPCs.

Other ideas could be to:
Split him off from everybody else, and give him a series of achievable goals that involve negotiating with NPCs. You could even let the other players play the NPCs in question. "You're ex army, you go see if you can get them to lend us a pilot and chopper, and we'll arrange the supplies."

Have an NPC, a woman or child (Newt from Aliens?) attach themselves to the character and follow him around, interacting at every available opportunity.

There's definitely a lot more that could be done to involve and engage this player. I think my friend puts a bit more stock in my GMing ability than I deserve, and I wish I could give him some better advice.