How about training the horse you are riding to do what you want.
Not to walk off untill told to. I do see the danger for you half mounted so to speak, and the horse needs to catch its paddock mate.
I agree with Roaddy and just let the horse follow and it sounds to me as it is the follower and is happy in that position but how does it act when front.
Here is some thing, you teach the horse the one rein stop, if you are unaware of it then it is getting the horse to freely give its head when asked for and allow it to be places by the riders boot nose to toe. When I ask that of my horse I give its cheek a gentle scratch and a few kind words, but what to does is, it disengages the rear end and the horse when taught will stand still. Both sides. If you know this then I am not trying to get you to suck eggs. I am assuming your riding is english style.
I also will assume you mount the horse from the left or right does not matter so ask the horse to bend its head to where what will be your toe position on the oppersite side you are mounting, then get on, the worst the horse will do is move in a circle in the direction you are mounting from. Then sit in the saddle for a minute before moving off.
I use this on my horse frequently, it is the horses safe place, and it learns it. It is also my safe place and i can get off if need be.
It also works on the horse that tries to step away form one just as you try to get a leg up.
Another is to train the horse when following, get it to stop and stand for a second then move on and increase the length of time untill it accepts being left behind the other horse. I know you may feel why should you train the horse but to me it sounds like if it up sets you so much, then the options are. As i said in an earlier post, get ready earlier and be the first to walk off. As Roadyy has mention just let the horse follow and enjoy, or train the horse to do as you ask, because, it is not at this time is it.
Good luck and if that all fails give him to a Kiwi female rider, she will sort him