If the lights are indeed 240V and the hood has an easily reached external fused supply (with a switch) - if it were mine I would hard-wire the lamps to be permanently on and control them with the external switch.
You could have Lamps plus Fan or Lamps on their own
But not Fan without Lamps - a small inconvenience at worse.
I guess that the circuitry you mention is to control fan speed rather than lights on and off - I guess too that the switch that operates the lights has failed but the rest of the circuit board is good.
Peccavi
May 2010