I had to have father-in-laws wall re-built when using SHMBO to direct me, she said she was watching other side.
However it was not due to reversing lights, I was going forward, and the second socket only works reversing lights, OK it could do split charging, work the freezer, and vacuum warning etc. However I am not really worried about that, I don't tow for long enough.
We find if fridge was on before we leave, still cold enough after 5 hours towing without power including the ice cream. Same on return, when we get home plugged in and often not emptied until next day.
For split charging to work with modern car you need an inverter, without an inverter it is so little energy transferred just not worth the effort, and reversing camera easier to have wireless.
I do have 13 pin, pain in the neck, as have to use converters for trailer and push bike light board. Some day I will replace with 13 pin plugs, which will mean the converters will no longer be required.
When the reversing light held the over run brakes off, then the second plug was required, but today it's not done electrically and I would not reverse at night without some one assisting. So one plug is really enough.