1980 450SEL W116

I am having an issue with restarting my car immediately warm/hot to about 5 minutes after shutting it down. The car starts great cold. If I drive to the gas station or if I shut it down warm or hot and immediately try to restart it, it won't fire up and I've noticed that I do NOT hear the fuel pump hum like I do when I start it up cold. I no longer try to start it now warm/hot until I've sat for over 5 minutes and when I toggle the key I hear the fuel pump hum (if I don't hear it hum, I turn the key off because I know it won't start), and at that point it fires right up.

*Should I always hear the fuel pump hum briefly before a start?

*Does this sound like a fuel pump relay going bad?

*Does this sound like a fuel pump going bad?

*Is there a temp sensor that prevents the fuel pump from running?

*Could this be a problem with the safety switch air flow sensor plate?

*Could a bad OVP relay be the problem?

*Could a bad O2 sensor be the problem?

*Could the warm up compensator (WUC) be the problem?

*Could the RPM sensor be the problem?

*Also, where is the fuse for the Fuel Pump Relay? Is it number 4? I can't find any reference to its location nor my particular problem.

Heading out to start testing. Thanks for any and all replies!

Well, the first place I went looking was for the warm up compensator. I have enclosed photos of what I found. I think since I have had this car this hose has been disconnected and I have no idea why or why I never noticed it except that one end had been buried and tucked under other hoses and the other hose end had been turned around and facing the wrong direction? But after cleaning out the cobwebs from inside the hoses and the WUC port, I reconnected them and after adjusting the mixture, the car is running better than ever and restarting immediately! I will check this tomorrow going from cold to warm and out and about.

Hose of Warm Up Compensator wrongly facing
forward.

Hose from (temp sensor?) found buried under other hoses. (Is this the thermovalve 40 degree C?).

One hose turned around and the other removed and it and its port are full of cobwebs.

Hoses repositioned and cleaned out and connected back together again.