I have a 1988 Carrier furnace model# 394GAZ0361OC. It was having problems on startup where the gas valve opened up and igniter started clicking but it was hit or miss on if it would light the pilot. I took the spark electrode out and cleaned it and along with the gas orifice. This did not solve the problem. I replaced the 3-wire pilot safety switch and the spark igniter but I am still having the same problem. Even with the new safety switch and spark igniter it still has a problem that it had before, and it's the one that many people talk about on message boards. That is, the spark igniter may click away for minutes before lighting the pilot. If I put a match to it when its doing this the pilot will light immediately. I noticed that once it fails to ignite and locks out I can unplug the 6-wire molex conector on the igniter lockout control board and as soon as I plug it back in it immediately sparks and ignites the pilot. Doing this to the igniter lockout control board seems to reset it to a state where it sends enough power to the spark igniter to light the pilot without hesitation but for some unknown reason it fails to do so on one of the next several startups. I looked at the lockout control circuit board and didn't notice any obvious burned up components.

You may very well have a bad connection on the board at the molex or in the molex itself. Bad solder joints are a common problem.