I don't know much about the S3 but it sounds to me like you have an incorrect plug for your S3... Some of the plugs are 3 segment - tip, ring, sleeve, and others are tip, ring, ring, sleeve, or 4 connections... Do you know for sure which one you have in the S3??? You might need an adapter cable to get from the 4 segment cable to the 3 segment cable... It sounds like your S3 uses a 4 segment plug and your cassette adapter is using a 3 segment (stereo) plug...
In terms of the "aux mod" for your 1500, the one I think of when that term comes up is where you physically modify your 1500 radio's input using a relay internally and bringing out a stereo input lead for your MP3 or phone device and a switch which operates the relay to change the input over from AM/FM to the aux stereo connector which now comes out of the radio...
Are you saying your using a cassette adapter to feed aux audio into your system??? Is this what you are calling the "aux mod" or does your radio really have the "aux mod" in it as shown below???
http://www.sheriart.net/honda/
Les