Using an AT Tiny to detect a specific voltage input and then drive an output
It would fall under a window comparator, there are ugly ways to do this with transistors, but really you would use an op amp for the problem (alternatively a dedicated comparator IC) this is usually a dual op amp IC and 3-5 resistors + power supply and some other components to drive your ouptut relay)

Its not overkill if it does the task and is within your scope of knowledge to solve the problem, &quot;when all you have is a hammer....&quot; in this case you would be using an NPN or mosfet to actually switch the relay coil leg to ground like in the first case.