There is no factory grease in it. There is a potting material inside that melts and runs out due to it overheating when it goes bad. It is common for the sticky stuff to get on the connector when it goes bad. I think you have found your problem. This may be the way yours looks like inside between the ICM and the coil pack.
How is that plastic part attached to the cable shaft? Is it just molded right to the cable shaft? My thoughts are to find a correct size ball and socket joint to replace the plastic joint completely.
Engine running and ABS light is on. No mention of whether AC works. Depends on value of 40k miles to you.
Pretty car but wonder if "strongest V6 3800 motor." means an L67. Right.