An isolator is not a relay. A true isolator does what the name implies, it isolates the two circuits, whether the ignition is on or not. Cheap products labeled an "isolator" but merely use a relay, are not an actual isolator, and really have no reason being discussed here. Manipulative marketing strategies do not make an isolator just a big relay.
Also, running dissimilar batteries in a circuit can cause problems, and is not recommended. If you dont believe me, check the links below.
"Connecting two battery banks of different amp-hour capacity together in series is a bad idea." -
ASK THE EXPERTS: Batteries in Series & Parallel | Home Power Magazine
"We would strongly discourage anyone from connecting batteries in series or parallel applications, if the batteries are not identical in age, size and type." -
https://www.optimabatteries.com/en-us/experience/power-source/can-i-connect-dissimilar-batteries-parallel/
https://www.quora.com/What-will-happen-when-we-connect-two-different-batteries-in-a-parallel
Cheers