I think trial and error is about right, but not totally. (Unless the archer knows very little, or has lots of time to experiment.)
First off, the bow recoils from the shot going off. That recoil also produces a backwards tilt of the upper limb. Place a weight in a position that will need to be lifted when the recoil acts upon it. One option is well out in front. Some will/may add enough weight to cancel almost all the upwards tilt of the longrod.
After that, the bow might be very front heavy. That tends to make the bow feel off balance at full draw and some weight further back brings the balance point close to the bow hand.
There is usually some torque in the system tending to cause the bow to flick, which shows as the the sight moving to one side or the other.
The longrod is well placed to reduce that, so it's a dual purpose stabiliser.
The stronger and fitter the archer, the heavier draw weight they tend to manage. That creates more recoil etc, and requires more weight to help control it. The archer is stronger and fitter so more mass can be added before they are beyond their best set up.
Running alongside those ideas, there are other options that control in a similar way. I could control the recoil back flick with a longrod pointing vertically down. That doesn't give the front heavy results so the bow doesn't roll forwards on release. Some go that way as they like the feel of that. I guess they would go back to a normal long rod if the vertical one felt great but didn't reduce groups.
I think "feels right" can be a very over used term. Some say that and know what they are talking about. Others say the same and have no idea what "right" means. I think they really mean it feels better than with no long rod at all. Some fit stabilisers and copy what they see others doing.
I am not blaming anyone for any of these things. It happens.
Cheshire?????
I think I visited an archery shop in Cheshire many years ago, I bought a carbon long rod.