Pressing accelerator causes electrical short

If they can do diagnostic work, an oscilloscope is needed to check Alternator AC ripple.
You can explain the situation and see what they say. I only mention the Alternator because that and the battery can cause so many more problems than people realize. If there is low system voltage for one, then all the voltage in the whole car is going to be low. AC ripple destroys Automotive computers because they are designed for DC voltage only. I'm sure an Alternator shop does more than just charging systems.
What you can do is on your way to the shop, turn some things off, see if the clicking stops.
It should not cost much to replace a $15.00 relay: they just need to figure out which one it is. Going through the wiring diagrams I could probably tell you how many are under the dash, but they can take care of that. I'm assuming the reason it's happening more when you accelerate is the alternator is putting out more current, and this relay is warming up faster and the problem is presenting itself more. Unless it's a bad ground wire that's just vibrating more with the engine at higher RPMs, so 2 scenarios there. But i don't think and hope it doesn't cost you much at all.

https://www.2carpros.com/articles/how-to-check-a-car-alternator

https://www.2carpros.com/articles/symptoms-of-a-bad-car-battery

https://www.2carpros.com/articles/how-a-car-electrical-system-works

I appreciate the thought but save your money to fix your car. I'm a religious person too, so no worries. I do hope the fix is cheap for you, having to do diagnostics from such a distance like this is not always easy. I do mobile diagnostics here in my area (NC), but here we have to go by what the person tells us they hear or are experiencing. So, it can be difficult. But I do really appreciate the thought. Thats good enough for me. I hope it goes well and let us know what the actual issue was. We like a follow-up when possible. I just hope Im not too far off on my diagnoses. =)

A tab on the rear-view mirror huh. Well, that's a first for me. Sounded exactly like a relay from the video, but I'm glad they didn't charge you anything. It does get tough to diagnose things not being at the car. But I'm glad it worked out good for you. Have a nice evening.