No External Display signal with Mini-Display-> HDMI cable on Mojave 10.14.6?

Have you done a PRAM reset, CMD+Option+p+r...

http://support.apple.com/kb/HT1379

In fact, do 3 in a row, takes a bit of time.

Intel-based Macs: Resetting the System Management Controller (SMC)...

http://support.apple.com/kb/HT3964

If PRAM and SMC resets don't help, I would suspect the cable or adaptor, those are inexpensive items (what type of cable and adaptor are you using -- cheap ones abound and some are not of good quality) that do sometimes fail. It is possible but unlikely that your Mac is the cause of the problem.

Try this...

1.. Shut the machine down.

2.. UNPLUG the power lead to the computer and any peripheral devices.

3.. leave it for 10 minutes.

4.. Hold power Button in for 10 seconds

5.. Connect everything back up and restart

You are plugging the mini-display end of the cable into your Thunderbolt port on the Mac. I believe for a 2012 iMac that would be Thunderbolt 1. You can connect other devices to those Thunderbolt ports, have you tried that to verify that they are working? You've pretty much eliminated the cable and the monitor, the only thing left seems to be the ports on the Mac (which I originally had thought was the least likely to have failed). Try About This Mac =>System Report to check on the Thunderbolt ports, do they show? Those ports, if they are like the ones on my 2013 MacBook Air, can provide up to 10 Gbps, can you connect an external hard drive, for instance (may require another adaptor, but that is cheap compared to what you might be facing if the Thunderbolt ports have failed)? Or perhaps a different monitor?

A System update or Security update does not break physical things. Those updates basically do a lot of copying and deleting files, just like you do yourself, but it is concentrated activity, and thus can cause temperatures to rise (especially in compact machines like laptops and iMacs) for a short time, which can cause an aged weak solder joint to crack, for instance.

Your 2012 iMac is classified as "obsolete" by Apple, which means they don't support it anymore and don't provide parts anymore. Although you can get some parts from third party vendors, maybe. I'm just mentioning this to raise the possibility that something has worn out or failed in the iMac to cause your problem. By all means, test those ports even if you have to take it to an Apple Authorized Service Provider. By the way, I'm hoping your iMac is healthy, it's a nicely equipped computer with the Thunderbolt ports, USB 3 ports, WiFi n, graphics, etc. (some even came with flash storage). I have some "obsolete" but still very functional machines, a 2008 iMac, 2010 MacBook Air, a 2013 MacBook Air, all with flash storage now and still quite peppy. I would try BDAqua's SMC reset again, hopefully will revive it.