It's not the pump, though it will aggravate the symptom. It's the mixing valve in the WH and it's common with that WH.
Your particular WH heats water much hotter than a standard unit. Then it uses a mixing valve (which depends on consistent flow) to blend cold water into the hot water outlet in order to keep those temps in check and give more usable hot water overall. That's why your is referred to as a "16" - it gives you the equivalent of 16 gallons of hot water.
It's that fancy mixing valve that's causing the fluctuations. It probably has hard water deposits/calcium built up in it.
You need to replace the mixing valve.