How far have you got to travel? If it's not far, I'd just get him to get a cab or if you must pick him up arrange to text him your car park location, stay in the car and get him to walk to you.
I've not picked up there but have been dropped off in the Premium drop off which is right outside the terminal. I just looked this up for you and the premium drop off (Which is where I would want to pick up) is apparently drop off only. They have cameras but I don't know how well it's policed.
The nearest car parks are a bit of a walk (it says 1 - 2 mins on the website I am suspicious of this timing see below) but I think that's an exaggeration. When I was dropped off the taxi said to me I can drop you here (free) but it's a walk or you can pay for the premium so I said I'd pay and he drove on. We drove past what seemed to me to be a long unpleasant walk with luggage (a souless long narrow pavement with hordings on one side and on the other the road I was being driven down). I was glad I'd say I'd pay.
I don't know the ins and outs of it like I said but personally I wouldn't be wanting to walk round there alone that late at night. It has a sort of creepy goods road/warehouse vibe if you know what I mean. Those sort of empty souless places that are dead.
In the day it looks like it would be a bit of a pain in the arse too but less creepy.
https://www.birminghamairport.co.uk/parking/drop-off-and-pick-up/
Like I said I've not done it but from the driving route, it didn't look like a 1 or 2 minute walk to me more like 5 mins if you were close or 10 mins if parked further. I would defer to any other posters who can give you more info from their own experience.
The whole thing looked utterly fucked up to me. Why they wouldn't have a drive through for both drop off and pick up for people (Which they used to have in the past) is insanity