I am not aware of what they use in terms of driving horses ponies or what ever over there BUT here
We call them lines not reins. I have heard some call them reins but do not correct them as some do.
Hoopla is correct on most her post although depending on the type of driving lines can and do touch the rump and sometimes do not. My horses and the horses I trained in the past if I am just pleasure driving my hands are relaxed, when Im working position is different.
There is no way to have a straight line from bit to drivers hands when jogging in a sulky or race bike without lines touching rump or even going along the side of the rump. But can when driving in a buggy that sits much higher up. Also if just pleasure driving ( not showing ) a simple egg butt bit or snaffle bit is fine. I jug in what we call a easy bridle.
To the OP since he has been atleast driven you can start by long lining him from the ground to get him back on track. I would get him working on the ground more. Then have him correctly fitted for a proper harness that you intend to use it for. As well as cart or buggy.
Oh and my experience is :
38 yrs in Harness Racing
12 years in pleasure driving. Trained under Heike Bean for 5 years.
OP enjoy your horse and be safe.
Hoopla look forward to other posts and its okay to call them what you want as so will I.
Others its okay to have opinions likes dislikes etc etc that's what makes this world go round if we all agreed there would be no wars no debates no hate. What a wonderful world that would be right?