On some vehicles, the turn signal switch opens off the brake signal to let the turn function operate. This could be the problem. There may also be two feeds off the brake switch, one for the third light, the other to the turn signal switch. Check both feeds for 12V with brake applied. You may also find the cruise switch located with the brake switch, don't follow the cruise leads.
'05 Voyage, W20, SMI, '06 CR-V
Ginger, the cat --Daisy, the dog