Ok, I just pulled the manuals I have on file for the Tundra. There actually was NOT a "factory" installed keyless entry on the 2002-2006 model years, they were all dealer or delivery port installed so unless the module was already added to this truck it will NOT program this remote to the truck.
If the system DOES have the module then this is how to program the remote to the truck:
-Driver door OPEN and key out of the ignition
-Insert key into ignition and remove 2 times (do NOT turn the key just insert)
-Close driver door and reopen 2 times
-Insert key in ignition 1 time and remove
-Close and open driver door 2 times again
-insert the key into the ignition and LEave it in, now close the driver door.
-turn the key to the ON position (not start) and then back to ful off position and then remove the key
At this point if the truck DOES have the keyless system then the lights will flash one time and the door locks will cycle one time. If this does not occur then the truck never had the system installed and you cannot program, there is no need to proceed. If it does have it then continue:
-On your remote push and hold BOTH the LOCK and UNLOCk buttons at the same time, hold these 2 buttons for 1-2 seconds, then release these buttons and push the LOCk button one time, the buzzer will chirp one time to confirm programming, then close open and close the door to end progamming mode.