Typically, the pyro detector produces a small signal that is amplified and filtered by one or more op-amp stages then fed to a comparator. There will be some delay mechanism in or after the comparator that sets the 'running time'. Unfortunately, without a schematic it will be almost impossible to determine which components are setting the delay although if they are found it is likely that it can be changed. Being surface mount construction might make it difficult to work on.
You need to trace the schematic, as the pyro end will not be responsible for the timing, I would suggest starting at the 'output' end and work backwards. The black box on the lower left side is probably a solid state relay and it looks to be driven from U1 so that would be a good place to concentrate on.
Brian.