Humm. They put the relay on the guages line.
Sounds like the wrong isolator relay to me. or wired wrong... Or you got a bad one,, Which of these 3 I'm not sure.
The problem is the isolator relay looks a lot like a starter solenoid, in fact physically they are often identical.. Electrically they are NOT, a starter solenoid will overheat and burn out if left on too long, exactly the symptoms you have. (It is the coil that burns out, not the contacts) Oh, it can haul the current, no problem there. But the coil is not designed to be engaged for more than about 1 mniute or less.
Home is where I park it!