I had the exact same thing happen once and have the same combo (Garmin G3X & ACK-04). My wife got the phone call from SARSAT while I was still flying. I called ACK and they told me the same thing. ACK said it wasn't their ELT but the Garmin GTX-23 transponder that causes this to happen. My transponder antenna cable was too close to the ELT remote switch cable. They said to move the two cables as far apart as possible. I ended up fabricating a four wire shielded cable for the ELT remote switch and have not had a problem since.
Eddie, as best I know this is only a problem if you have a Garmin GTX-23 transponder and a ACK-04 ELT. If that is what you have at least you know it before you install everything.