@Demian Johnston
Nice job collecting data while trying to diagnose this issue...
It is indeed baffling as to how it would be possible for the EVSE's to behave differently (given the very limited functionality of the J1772 interface). And, even if they do behave differently in some obscure way, how could this impact the 12V battery drain like you are seeing?
When the EVSE is connected to the vehicle, but NOT charging, the pilot signal should be a 1 KHz square wave who's duty cycle informs the vehicle of the current capacity of the EVSE. It seems like this should be identical with either EVSE.
While thinking about this, I ran into this post on Reddit:
https://www.reddit.com/r/VWiD4Owners/comments/11w5yh6/tesla_wall_connector_j1772_issues/?rdt=47680
Although not complaining of LV battery drain, this person was experiencing constant clicking / cycling of some sort, which he felt was the relay within the EVSE, turning the AC line on and off every few seconds.
At the end of the reddit thread, he reported that he contacted Tesla, and this problem was resolved by installing a firmware update (23.8.2/20230310). Perhaps Tesla does have a fix that might somehow relate to your unusual issue.
I also agree with the general feeling that your 12V battery is probably toast at this point.