A 2way checkvalve has 2 inputs and a single output. Whichever input is greater slides the core out of the way and feeds the output.
your issue is the top 2way checkvalve under the drivers floor(behind the grill). When you release the brakes, you APPLY park air to one side of that 2way. The other input of the 2way connects down to that red front gladhand. The center output of the 2way feeds your park brakes. So either your park air control or a towing vehicles trailer air control can release the brakes. The air feed to presurize the air system on your truck from a towing vehicle is Td off that line near the red gladhand thru a checkvalve So a towing vehicle can charge your air system.
what is happening is you are applying park air and it is leaking past the core of the 2way and escaping thru the vented front gladhand. If your gladhand wasn’t vented, that leaking air would pressurize that line like a small air tank, and when you released your park air control in the dash, to set the parking brake, this stored air would flip the core and keep the parking brakes released just as a towing vehicle would with their park and trailer controls on.
this will keep your park brakes from setting until all that stored air leaks away. The giveaway for this is you release the park air to set the brakes, and the park and emer lights don’t come on
i would pull out that 2way and first disassemble it and look for some crap in it. But ods are it is just old and you will need to replace it…
A clogged blue service gladhand works the same way in that the line stores air like a tank if the 2way leaks past. Except in this case, you step on the brakes, the service air applies the brakes and charges that line to the gladhand, and when you release the pedal, that stored air continues to apply the brakes via the 2way, just like a towing vehicle would… untill the air leaks away.
common issue, thats why the gladhands must be vented…
i did a video on deleting those gladhands that explains how they interact and shows you the parts locations… the top 2way is almost easier to access by removing the grill…