You want to find the mid-points of the wooden uprights behind the plasterboard.
This is what you will want to screw the hook board into.
Yes, this may involve re-drilling the hook board.
The wires will generally be going vertically between the uprights, not across them.
In this scenario, if you cannot see the vertical rows of plasterboard screws to show the line of the uprights, my preferred approach is to use a thin screwdriver to experimentally poke holes in the PB. It will simply push through anywhere between the uprights, but will not damage any wiring or pipework. If you have hit an upright, you will not be able to push it through. Give it a wiggle left and right to see if you can feel an upright. Move left or right, repeating this till you find an upright. Try to find the other side of the upright, and hence determine the mid-point.
The next one will usually be 16 or 24" / 400 or 600mm away, depending on vintage.
You will end up with a horizontal series of tiny holes which will be hidden behind the thing you are mounting. Un-hidden holes can either be filled or ignored, depending on where they are.