What you are asking is not really practical or safe!
The system was not designed to run without a display present as it controls the air flow internally as well as protect you from high voltages from the power supply.
The GPU logic is not designed to run without the internal displays load, you will damage your system running it in this state.
I would strongly recommend you get a replacement display for your iMac or put the original one back in.
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=== Update (01/16/2021) ===
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'''Maybe this will help you.'''
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I’m sitting on my couch watching TV using a 15” 2012 MacBook Pro. I have a small project running on my MacPro in my study as it takes about an hour to run I can watch things remotely connecting to it.
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This is a better method than trying to wire in your second system into your iMac so you can access your second systems video feed.
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I don’t recommend [https://en.wikipedia.org/wiki/Rube_Goldberg_machine|Rube Goldberg machine] builds when simpler methods are available.
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If you want to have a iMac like display why don’t you look for a junker which you can convert into a display. You have the needed kit already so all you need is a case, power supply and a good display!
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Then you can have a matching unit besides your current iMac! You could even use it as a second display to your iMac via a mDP cable connection.
What you are asking is not really practical or safe!
The system was not designed to run without a display present as it controls the air flow internally as well as protect you from high voltages from the power supply.
The GPU logic is not designed to run without the internal displays load, you will damage your system running it in this state.
I would strongly recommend you get a replacement display for your iMac or put the original one back in.