Okay, yes, hot-cold and the motor moves as it should So we can rule that out.

I don't think it's practical for me (if I could do it) or to pay the mechanic to change every vacuum hose.

But I will attempt to rubber elbows connecting the line as well as the "Ts" (I only saw one.)

Any help on what the check valve looks like and its function?

 

Iour check valve will look very much like this.
With the motor cover off, look on the passenger side of the intake right below the throttle linkage, there'a a vacuum line coming off the side and to like a "Y" the check valve is right there and the vacuum lines split off to serve the reservoir and one i ferget where it goes at the moment. I'll probably say it wrong here but the valve prevents the engine from using up too much vacuum resource that the a/c and cruise control also need when the engine has a load on it.... that;'s my basic understanding of it

 

It looks as if (and I've often been wrong about this sorta thing before) it's an easy thing to swap out, provided I make sure to remember the direction.

From your experience, is this a generic valve -- or is it Dodge specific?

 

I just googled check valve for dodge 5.9 and this is one that i saw that looked about same, but no not specific for us i don't think.
Try napa,auto parts, they should have one, I bought mine there but seems for me there's something else going on that i haven't found yet.
The member here goes by "moparite" and helps out has recently posted the correct part number in one of these van threads or the 2nd gen trucks. shoot him a private message and ask, I'm sure he'll be glad to help with the part #

 

Thanks you've been very helpful, going way beyond the call of duty!

 

This is the one i used to replace mine. Only difference is it is reversed so you need to see witch way it allows vacuum to flow before you put it on.

https://www.napaonline.com/en/p/NDP7301349