Recently I will turn on the water, a mix of hot and cold to get temp right. Then the water will pulse between hot and cold. First experienced it in the shower, then the bath sink, and then the kitch...
I had a similar issue and found that I had a huge amount of calcium in the tank. I believe the incoming water was stirring up the calcium and momentarily blocking the outgoing hot water. I never did figure it out for sure but it did stop after emptying and cleaning everything out.