Why would a 'service engine soon' light keeping turning on and off in a 1998 Dodge Neon?
Take it to a auto zone and find out what codes are stored. If there are no apparent problems or noises, try having the oxygen sensor checked. It doesn't have anything to do with the car running properly, it's an emissions control device. If you turn the ignition key on,off,on,off,on with in a five second period the service engine soon light will flash a code number to tell you what the problem is. you can get the trouble codes in a Haynes repair manual page 6-3.