My guess would be since that looks to be a millivolt heater, it has its power provided by the pilot flame. You could do some troubleshooting by temporarily bypassing your pressure switch which what your first picture is. First make sure your pump is on, water flowing through the heater, have the heater off, pull the two wires off the pressure switch, use a piece of wire to jumper those wires together and turn the heater on to see if it will fire up. If it does you can pick up a pressure switch at a local pool store and replace it. If it doesn't fire up. it could be some loose or oxidized wiring that isn't making a solid connection. Please do not run your heater by bypassing the pressure switch as a solution, because the pressure switch is there for safety, it will ensure that water is flowing through you heater to stay lit, if it is bypassed and the pump shuts off, your going to melt down your heater, but then again the high limit switches will kick it off. (unless they have been bypassed, since I've seen that before, along with most other safety switches bypassed)