Hi pNuker,
If it is a relay that is energized when the key is on have someone else turn on the key while you listen for a "clunk". If you hear the clunk then check for power on both "sides" of the relay. If there is no clunk check to see that the small wire has power when the key is on. Mine had a fuse before the relay that I've caused to be replaced by auto reset circuit breakers.
Relay type isolators do fail and contacts do burn. My Ford OEM one lasted less than a year, in spite of it being rated for 100 amps. The contacts were in poor shape. The "intelligent" design folks put the relay down below the starter battery so the battery has to be removed to service or check the relay. Of course you can't check it with no starter battery. The one I used to replace it is a lot better made.
I would not put my inverter through a shunt. Too much chance of a surge taking out the shunt and leaving me without cabin power. I would have a heavy duty manual switch on the inverter as well.