I don't know if it was the mecha designer's intention or not, but in the anime the GM does NOT draw its beam saber with its left hand, because that hand is already occupied with holding its shield!
Did the mecha designer make a mistake and originally intend to put the beam saber socket on the GM's right side so it could be easily drawn by the GM's gun arm?
I was an avid player of the Federation Vs. Zeon Gundam arcade game, and it looked quite funny to see a GM reach with its right hand to its left shoulder to draw the beam saber. Guess that comes with being too faithful to the original's designs.
I like Yoshikazu Yasuhiko's (he's the guy currently drawing and writing the excellent Gundam: The Origin manga) version of the GM myself, frankly. His version puts the saber on the right shoulder, and replaces the dorky chin with something MUCH better. Best of all, Amuro Ray gets to kick Char's ass with only a GM in Vol. 9!
reese said: Well if the shield and gun are lost, I suppose it is up to pilot to decide which hand to draw the beam saber from.
The difference being that I seem to recall that the GM had a way to easily holster the gun, but not the shield. That's why I would think putting the saber near the gun arm's shoulder would be the wiser move.
You should really take a look at the version of the GM from Gundam The Origin and see how improved it is over the original MSG anime GM.