Joe,
Much good advice already.
I suggest a simple test.
Whilst alongside and with all other wiring complete just switch the pilot on and see if it works.
If it does then the ground connection specified does not form part of the power supply wiring to the pilot and is only a means of shielding the pilot's case.
From a designers viewpoint he is wishing to do his best to protect the pilot from outside influences. If the pilot is on sale in Europe then we have a specification requirement for "Electromagnetic Compatibility". I expect similar in the USA.
What this all means is that the item of equipment should neither cause interference problems with other equipment, nor should it suffer from interference caused by others.
To a certain extent protection from external interference is an unknown quantity so the 'best' grounding possible is desirable and the conventional way is to use a flat braid to, what is hoped to be, a 'good' ground point - and 1/4" wide copper braid is deemed to be satisfactory for all but the worst interference.
In fact just about any heavy gauge wire will suffice unless your system is being blasted by high power radar pulses - and if it is then even braid would probably not be enough.
My advice is to either buy a bit of braid from Radioshack or use some heavy gauge yellow/green wire and forget about it.
A Google search showed this site selling cut lengths of 3/8" tinned braid (best for marine) at $0.45/foot.
http://www.dxengineering.com/products.asp?ID=175.