You need to jumper pins TE1 and E1 to enable the onboard computer to retrieve the codes. From that point, you are counting the flashes of the check engine light to extract the codes. They do make a handheld scanner for OBD-I cars, but they don\'t always work correctly.
More information can be found online - just search for Toyota and OBD-I.
As for what is going on - could be nearly anything. Not coming on right away just indicates that there is multitrip error detection. Most CEL codes need more than one failure event to cause the check engine lamp to come on. That latency makes it appear that the CEL is \"timed\" to come on. Have to pull the code to find out what is going on.
2002 Corolla S, Silverstream, 1.8L 1ZZ-FE (VVT-i)
2003 Matrix XRS, Cosmic Blue, 1.8L 2ZZ-GE (VVTL-i) - RIP
2009 Matrix XRS, Blue Streak, 2.4L 2AZ-FE (VVT-i)