HI Dutch guy with a almost Danish name ( KarstEN )
You must have a hard wire kit with low voltage protection, if you have the camera to a always on cigarette lighter then it will just keep going no matter the voltage.
Some cameras have a low voltage cut off in the camera itself ( often 12 V cameras ) you should not use a lover cut off voltage than 12.2 volts if you have a regular lead/acid battery in your car.
Not familiar with any Garmin dashcam other than a little stuff i have seen on the internet, among those problems with the mini model and parking mode ( runaway heating ) but of course that was in the early days, i do not know if this have been fixed with harwdware updates.
The guy i saw on youtube was happy about his mini, aside the the problem that arise when trying to use parking mode.
Also yes how long you can run parking mode depend on a few things.
1: the size of your car battery.
2: the state of your car battery.
3. how much power the camera use while parked.
Using parking mode of course have some demands, you must drive and restore the power you have used, so of course you can not use parking mode for 23.5 hours every day and only drive 30 minutes, or even worse.
Normally to use parking mode you need a hard wire kit that are tapped into either the OBD diagnostics port, or are connected to your fuse box, the low voltage protection are normally in the hard wire kit, at least for 5V USB powered cameras, so the 12 V to 5 V converter are also in the hard wire kit, where as for regular kits the 12 v to 5 V are often in the plug you put into your dashboard socket.
That do indeed look like a 3 wire hard wire kit, is it from garmin ? usually it is recommended you use hard wire kit from the same brand as the camera.
There are some universal hard wire kits, some of these can be very bad, might not even have a select-able cut off voltage ( normally a switch you can slide to 11.8 - 12.0 - 12.2 - 12.4 Volts )
11.8 are a very low cut off voltage, that low the load on a lead / acid battery will be high if you use and hit that every day, it might also make starting your car in really cold weather a problem.
12.2 volts is said to be 50% of a lead acid battery.
It might also be you have the two 12 V wires connected wrong or not suited fuses, especially with very new cars, choosing the right fuses can be somewhat of a problem.
If you write what year / make - model of car you have, and what fuse numbers you are connected to, then @jokiin are often very helpful getting alternative suggestions from a tech he know
Is there any way to see if the files made while you are parked are actual parking mode recordings, normally a parking file will be shorter or have a lesser bitrate then regular driving recordings.
Some cameras also handle files in different ways, so one brand might add a suffix to files to identify, so a "P" at the end might suggest it is a parking mode file, other brands but different files in different folders.
The one SG camera i have and use parking guard, as i use low bitrate regular footage for parking mode the parking files are same place as regular files are, but easy to spot as they are only 118 MB in size VS normal files that are 350 MB in size ( for a full 3 minute file )
Events created by G sensor while i am parked go in a folder named RO ( Read Only ) this SG camera also here deal in full files so it save 2 from each camera in the case of a event, other systems might use a buffer, in which case the event files will be a lot shorter than regular files.
But otherwise the SG camera of mine do nothing to the naming of the files.
As i recall Karst are also a kind of rock, and for us Danes the Dutch also rock as if it wasent for them we would be Swedish today.
from memory the low voltage cutoff options are inside the hardwire kit on the Garmin, need to take the cover off to access, the Mini has known problems with parking mode though, expect problems if using parking mode on this model
Inside thew Garmin HWK is a 'shorting bar' across two pins to set cut-off voltage. Two lines of pins allow the bar to be set to different voltages which are marked on the PCB. 4 small phillips scews hold the case together. Just lift the bar straight off the pins and push it back on the pair you want to use. Not too hard to change settings but definitely inferior to the switch accessible without opening the case most other companies use.
I assume you would just do this one time ( set cut off ), but maybe if the kit are default to 11.8 thats not good.
I suppose if OP set the parking mode to off, and the camera turn off when he shut down his car, the HW kit cant be wired wrong, or on a fishy acting fuse.
The problem as mentioned in the video i dropped seem to be coming out if parking mode, but then the camera needing a reset to be operational again, but it dont sound like that is what OP experience.
So i was "fishing" for some answers as to what kind of files it generate while supposedly in parking mode.
Not many with this system in here, so i can only speak in general terms.
The garmins are they locked to 1 min files or is there a choice with those ? if it generate the size ( length in minutes and file size ) then it cant be in parking mode as i dont recall it having low bitrate allways record.
So any events generated while parked ( motion or G sensor ) should be a array of sizes at least if it use motion detect.
Best thing is probably to get off parking guard to start with, bleeding your battery dry all the time are not healthy for it.
I have both a Garmin Mini dash cam and Garmin 56, each wired to a Garmin hard wire kit with parking mode activated for the minimum time period of 2 hours and I have never had any issues with the car battery draining. These are installed as forward/rear facing cameras and I have not adjusted the cut-off voltage and I have had trouble free operation with no over heating issues.