If it is an electrical gremlin - could be pretty hard to nail down - the MIL may not light up if the sensor is not grossly out of spec.
The pulsation damper looks like the choke from an older carburator setup - should be on the end of the fuel rail with a screw on the top of it.
The pins to jumper to get the acess the self diagnostic system are TE1 and E1 under the hood (shoud be marked in the lid) - ignition to ON, but not running - jumper the connector - then read out the flashes on the CHECK ENGINE light (single flash every 1/4 second if OK).
Might also want to take a peek at the ignition system - other than fuel issues - the Camry was pretty much trouble free (5S-FE motor).
Good Luck.