The Spares & Technical section on this website, in the Technical information section, second item is Hesketh V1000/Vampire workshop manual (kind permissiojn of Mick Broom) has a page with Modification to RETA IGNITION SYSTEM Dec 88. Wiring diagram for a double pole relay in the wiring to the coils, so that 12V is applied to the coils when the starter button is pressed, reverting to 6V when starter button is released - standard sytem uses 6V coils in series.
Is this the mod you're looking for?
Haven't done it myself.
Dave H