I can see Gillick accepting a team presidency within a year or two maybe Seattle or Toronto.
As to qualities in a so called "clone" for our GM well the following would be included:
1)Smart trader:Must be able to wring the most value for the least offered from any partner league notwithstanding.
Must also be willing when making trades for players who the club will be interested keeping longer term than their present contract i.e. Bedard who require top value to get he/she must insist on the 72 hr sign or no deal clause be in force.
2)Top contract negotator:Able to work reasonable deals with unreasonable agents.
Futher workout extensions that don't totally preclude any ability to trade later because of salary and/or length i.e. Johjima.
With those same reasons in mind (salary and/or length)when signing FAs or making trades as well i.e. Sexson/Vidro.
3)Must be able to rebuild and maintain a thriving MiLB system capable of feeding the talent needs of the big club and having enough surplus to allow trades with hurting the pipeline supporting the big MLB club.
4)Know player development well enough so he/she can make as an informed decision as possible when drafting or trading etc......no matter the level from instructional to MLB.
5)Be able to judge with confindence the best time to trade a top veteran for the most value and benefit for your club not the other guys.
He/she should have a policy that a cross between Beane's in Oakland and the great Dodger GM Branch Rickey's better to trade a player a year too soon than a year too late.
6)Should instill something that in these days of FA etc.... is rare LOYALTY to one club like what you see in Ichiro and when he played Edgar Martinez.
Of the qualities above Youth has a place there as well but gender isn't a factor to me if Kim Ng can meet the majority of them great I'm all for her.If LaCava fits the bill also great etc......
However no matter WHO gets the job the Terrible Twosome MUST agree to non interfence clause unless specifically listed and let the new GM do what MUST be done to fix the ship both short and long term plan.
Hopefully leading to winning then contending and finally a WORLD SERIES.

In the list of qualities #3 the line should read "to allow trades WITHOUT hurting the pipeline that supports the big MLB club".

You could also break them down into how they evaluate talent:

Pat Gillick - scouting, hands on
Ned Colletti - scouting
Andrew Friedman - sabermetric
Theo Epstein - sabermetric, scouting

So if your looking for one to clone, I'd take the GM that will pull from multiple sources to determine a roster construction, Epstein.

I also believe Kim Ng is a clone of Epstein that they are interviewing.

Theo Epstein assuming he did well with the Padres who didn't have as much money as Boston.

I beleive the top 4 possible gm's would have to be the 2 from arizona,the mets guy(anybody that can hang in the ny should be good here),and of course the Kim Ng.Although with the mess Bill left behind and the starting from scratch method that the mariners are heading into the offseason with,I'm not 100% sure Kim could bring it around.If she does endup our gm she has a one time shot,a 50-50 chance of bringing it around...And maybe just maybe a females touch is all the mariners need right now to get back on track...But whatever the gm outcome is you have to be able to build around key players:Raul,Felix,Jeff,And Brandon...And of course Ichiro