Gas gauge needle flutter

[Greg63]

I don't know if this is a unique problem or not, but I did search through other threads and couldn't find a situation similar to mine.

In my '63, I installed a 21 gallon replacement gas tank under the bed. I used the sending unit that came with the tank, and it functions well - to a point.
The gas gauge reads accurately in respect to my fuel level. My problem is that the needles flutters VERY rapidly at random times. I just changed out the stock gauge with another stock gauge. The flutter is still there, just not as severe.
I know the signal from the sending unit is getting to the gauge, but I have no idea why the needle flutters.
Can anyone shed some light on this?
Greg.