Hello, Simon,
An early system 11 game such as Fire has four separate 'General Illumination' circuits, with a block of four fuses (5A) just below the power supply pcb, upper right hand side of the lightbox. The circuit may well be controlled by the relay on the p/supply board, with connections at the lower right corner of the board. As above, check for burnt connections, which were/are common with this area, due to the higher than usual current carried.
'Scuse my asking, but are the lamps which aren't working small, or do they have large round glass envelopes, like a car tail-light bulb?. The former are the G.I. lamps already mentioned, while the larger bulbs are 'flash' bulbs which only light momentarily (if at all, with this games appetite for them), and are powered by the solenoid circuits.
Fire used to consume these bulbs at an awful rate, due to the resistor arrangements, which are supposed to restrict the current, being the wrong value (too low). With Fire, Williams began to wire the lamps as a pair in parallel, rather than in series as on previous games. But the limiting resistor for each circuit remained the same, when it should've been increased to counter the lower resistance of having the bulbs in parallel.