hornet 564t random auto starts

Vehicle: 2005 Cadillac CTS Alarm/Auto Start: Hornet 564T Issue/Problem: The car randomly auto starts and runs for hours and sometimes overnight. Our initial thought was that the remote was in the owners purse or in the hands of her kid and was accidentally entered into timer mode. They tried stepping on the brake to exit it from timer mode, but the issue remains. We have heard there is a mode that will start the car if the car battery level is too low or the temperature drops too low, but have found nothing to support this. This also happened about a year ago, but I'm not sure what resolved the issue. The 2-way remote is missing and before it went missing, I know the battery in it was low and the remote beeped every few minutes. Any help would be appreciated. Thanks!

it could b in 24 hour timer mode it starts every 24 hours. to exit press lock and start butttons at same time, theres also regular timer mode which starts every3 hours but stepping on the brake exits this. how often does it start?

what you could do is either flip the toggle switch (if you have one) or reset the system buy pulling the fuses for 10min and putting them back it to reset the system but only the fuses on the remote start power wires