<VV> floating fuel gauge needle

[Landis, Art MR]

I'm sure this is a common problem but being a novice please indulge me.  I
have replaced the fuel sending unit when I refurbished the tank and my gauge
was working just fine for a few weeks.  All of a sudden the gauge has
started floating slowly back and forth and is rarely accurate.  Does this
sound like the gauge itself has gone bad?

 

66 sport sedan, 140, PG