Best I can tell, the timer relay has a double acting relay coil and a set of Form C contacts. It is either energized in the run position, reversed energized in a timed stop position or unenergized in a neutral "break" position when power is off. Similar to how the 3 way current limiting relay in a electo-mechanical voltage regulator works.
In the "run" position (key on, switches made), 20amp fused current flows from the key switch - through the safety switches to the timer relays "run" coil windings which pulls the run contacts closed which passes the 15amp fused current to the timer circuit to charge it up.
In the "stop" position, (key off and/or one of the safety switches open) the 20amp fused current is removed from the "run" coil and the charged up timer circuit is sufficently charged up enough to overcome spring tension and pulls the contacts in the opposite direction, and "makes" the "stop" contacts. The 15amp fused current is now passed on to the stop solenoid. Once the timer circuit hits a preset time (approx 10 -15 secs, probably dependant on some sort of capacitor discharge rate), current is then removed from the "stop" windings and spring pressure returns the contacts to their neutral position. This is how current flow is removed from the stop solenoid after the timer expires.
If one were to disconnect the electrical connectors to the fuel pump and stop solenoid, (or connect up a multimeter to the timer relay), you would hear/see the timer relay click into the "run" position when the key was turned on, then hear it click into the "stop" position when either the key is turned off or one of the safety switches is opened. Then after approx 10 -15 secs you would hear/see the timer relay "break" from the stop position and return to it's neutral "off" position.
Course since theres no schematic or troubleshooting reference on the timer relay this is just an uneducated guess. This seems to be the way the circuit works on my 04 BX23, your use may vary
