My hot water tank clicks after I use the cold water or flush the tolet, what is causing this?

If it is a "Instant Heat" type water heater, that is the contactor(relay) making high current connections. Since this is on your Cold side, could be at threashold or coincidence.
I have seen houses where the plumber acidently put hot water to the Toilet?
Do you have a Tank heater?

It is a standard 50 gal electric hot water heater.

My hot water tank clicks after I use the cold water or flush the tolet, what is causing this?
Tell us more about this "click". One click? A bunch of little clicks? Loud or soft clicks? Do the clicks come from inside the heater or from a nipple on top?
Give us all the details you have. Regards, Tom

There is clicking sometimes as things are heated or cooled, Metals expanding and contracting?

It did not answer the question, but told us of the expansion & contraction of items

I am trying to find the locations of sensors, I am aware of the sounds that hot and cold can make. Re-read the question please

From the top nipple, that's where the clicking noise sounds like it is coming from.

This sounds like a heat trap nipple. If it bothers you simply get a 3/4" brass nipple and change it out. Good luck, tom