GAC;
Didn't see anyone put something here. Was out for a short time, but here goes.
The bad news is; not ever heard of or ever saw a ciruit that'll do this.
That however isn't to say you could make a pseudo one.
If you're looking for a load sensing type of system you might want to look into a UPS type circuit but in reverse.
DamonHD has a working circuit , that senses the LVD of a battery set and goes into AC mode. SO something similar to that could work.
What you could do is wire a switch into one of the inverter's DC side and leave the inverter on, then when you want to use the light or anything else on it, turn the Dc switch on , the inverter comes on and you're all set.
Hope this helps
Bruce S