Indicator relay flashing relies on a set resistance through the 'circuit' to flash at the required rate. If one or more bulbs in the circuit has a dodgy filament the resistance will change thus changing the flashing rate.
The bulb fault light is showing because the overall resistance in the circuit has changed, therefore it presumes a bulb is out.
Chances are one bulb will blow very soon as the resistance isn't right. You can either change all indicator bulbs on that circuit or wait for one to blow and just change that one.
If an LED has been used to replace a filament bulb, this can cause an issue (but not always. It depends on the LED resistance).