In this case, though, in the powered-off state, it does not go to an out-of-range position, so I suspect there is something more to this arrangement.
The question is, I think, "what setting would be least likely to cause a dangerous situation, if the indicator failed and the crew did not realize it had?" My guess is that the least desirable "home" position is fully-open, if it would usually be important to have the cowl flaps fully open during takeoff and initial climb-out to avoid engine overheating. Fully-closed may also be undesirable, if there are cases when having them closed is important (maybe with an engine fire, to minimize airflow and keep the fire-extinguishing agents in place, or after an engine failure, to reduce drag?) Intermediate positions would be chosen with reference to the cylinder head temperature, so the specific reading of the cowl-flap indicator might be less important.
Or maybe its just that, for a differential instrument, the middle is an unbiased home?
I believe for this style of instrument, for powered off state, or severance of connection with the sensor, that middle was the unbiased home position, because rarely would you place the settings right in the middle for an extended period of time. There are several RPM indicators out there like this as well. I've got two very old 1950's era indicators for RPM that work just like that.
There are of course other instruments that do different things to indicate failure of gauge, failure of sensor, failure of connection, and so forth.
I have several of these older aircraft gauges, and other mechanical and analogue gauges from various devices in my workshop in a drawer, and taking them apart over the years, I can honestly say I have not found one from a particular manufacturer that is quite the same as another in mechanical operation from another manufacturer, and also mechanical differences between different instruments for different functionality. I've also found that when used in regular operation, i.e. wired up precisely how they are supposed to work, some instrument gauges would make a sort of wobble motion until they settled, like the amperage when applied would drop, come back up, go over, and then return to nominal. Old analogue circuits and capacitors hold charge, and take a while to settle, so it is always fascinating to watch these devices "do their thing" in their natural habitat.
My knowledge of aircraft systems, beyond tinkering with old gauges, is limited and I readily admit ignorance in most of this stuff.
The question is, I think, "what setting would be least likely to cause a dangerous situation, if the indicator failed and the crew did not realize it had?" My guess is that the least desirable "home" position is fully-open, if it would usually be important to have the cowl flaps fully open during takeoff and initial climb-out to avoid engine overheating. Fully-closed may also be undesirable, if there are cases when having them closed is important (maybe with an engine fire, to minimize airflow and keep the fire-extinguishing agents in place, or after an engine failure, to reduce drag?) Intermediate positions would be chosen with reference to the cylinder head temperature, so the specific reading of the cowl-flap indicator might be less important.
Or maybe its just that, for a differential instrument, the middle is an unbiased home?