For the shortest possible wait, go to DL on a non-EMH day because the M&G doesn't open until regular park opening. Get to bag check early (I'd say even as early as half an hour) so that you can be first through bag check and first in line at one of the gates. You really want to be first in line at the gates so that you can be at the very front of the rope.
Once the rope drops, you literally have to sprint and it's no joke.
HOWEVER...there was another thread here about a CM trying a more "controlled" approach of lining people up that backfired because it wasn't applied consistently across all the gates and rope drop locations. So be aware that they could be trying yet another strategy when you're there. Also note that running is technically against the rules at the parks...a poster here had her child knocked down/bloody nose by a hit-and-run during the M&G sprint. So if you choose to run (and really you kind of have to in order to have the shortest wait), be careful and mindful of those around you

And know how to get there. Fastest way is straight through the castle, then veer left and look for Olaf on the roof. You can also take the little paths around the castle (less traveled but not any faster).
There are 2 rope drop locations that I could see - one more to the left of the castle and one in front of the castle. I don't think it matters which you are at but the left side did seem less crazy. I was looking back at my video and there were a lot more runners bursting out of the rope drop that is more in front of the castle.
Anyway, we just did this last week and here's a breakdown of the timing: We went on a non-EMH day, regular park opening was at 10am. DH got to bag check at 7:30am (he was being extra cautious - I think he could've gotten to bag check at 8am and be fine). Bag check opened at 8:30am. He was first through bag check and parked in front of gate 9. The gates opened at 9:30am and he fast-walked to the rope. We were right in front at the rope drop to the left of the castle. I had the stroller with both kids and he had nothing on him. DH wasn't planning to run (we had a whole convo with another dad at the gate about how ridiculous it would be to have to run, and both dads agreed that they were above running). However, when the rope dropped and all the OTHER dads started sprinting, they broke into a run too. We met them just a few min later in line (it was already backed out to the 120 min mark) and we still waited 45 min. The dad after us in line said (and he was serious) that he could've gone faster if he wasn't carrying a bag...I looked and he had the family's giant diaper bag, LOL. It's just nuts. The CMs kept telling everyone that a 2-hour wait was GOOD and encouraged those in line up to the 120 min mark to stay put if their kids really wanted to see A&E.
Only one person in the party has to wait in line so I would just count on a significant wait and make the best of it if seeing A&E is truly a must do.
One other caveat - THEY ONLY GUARANTEE ONE PRINCESS. There, I said it. It's an awful feeling not knowing if they'll both be there until you get closer! It's just another thing to factor into the "is this worth it" decision.