I agree with Randy. A LM555 timer circuit should be able to trigger
the camera by itself. I thought the Vout on the pulse was the same as
the voltage you put into the chip (minus a little bit, schematic I
found says you put in 5V you get out 3.3V). If it (voltage, current)
isn't enough to trigger it, then you have the output of the LM555
trigger a transistor that allows electricity to flow and press the
button of the camera. You are looking a a couple dollars of parts and
a crazy battery life (6-15 mA, so a 300mAh would last you 20 hours at
the high end)
As for the problems with the relays, unless the relays are bad, I
think you have a very fine solder bridge somewhere. I would run a
multimeter with a connectivity setting (or use the voltage) around
your board. Compare your working one to the one that is not.