Perhaps the new man, whilst refered to as a General Manager, is to all intents and puposes a Director of Football, a la David Pleat when at Spurs.
It doesn't neccesarily mean that he will pick the team but possibly reserve the right to discuss selection with "the coach"?
Danny Williams was for some years the general manager at STFC.....it was what is known as "moving upstairs" basically the job consisted of doing work that nobody else seemed to be job described for.......doubtless he offered his thoughts to the manager and probably scouted a bit and suggested players, after all he had a decent record of talent spotting.....Peter Noble, Joey Butler, Roy Carter, Chris Kamara, Ray McHale etc etc.
Its seems to work, when the GM is a senior figure with no real interest in sticking their oar in, having been there and done it.....it also maybe helps if the coach is young and inexperienced......Lenny Lawrence and Trolly seems to work at Wovers.
An abilty to speak English may also help.