You have dirty contacts on one or both of the sender units. The contacts are
wiper-like thingies that work much the same as a rheostat -- potentiometer.
They could work exactly the same way, but saying "much the same" allows for
error.

In any case, my E36 did precisely the same thing as yours is doing. I
removed the left-side fuel sender unit -- mostly because I felt it would be
easier -- and cleaned the contact wiper with a combination of contact
cleaner and a business card to mimic very fine sand paper. I cleaned a
significant amount of black crap from the contact patch and wiper are, and
the sender unit worked properly after that.

The left side and right side sender units work the same way, but the right
side unit also contains the fuel pump. There are two sender units because
there are two discreet gas tanks in the car. There is a pump system that
tries to keep the level in each bladder equal, but there are two senders
none the less. (I like to think that if the levels could be kept equal, then
only one sender would be required.)

To gain access to the senders, remove the rear seat bottom, and carefull
pull back the tar paper material to expose the round cover. Remove the cover
to expose the gas tank. Take off the hoses and wires that are connected, and
remove the ring that holds the sender unit in place. The sender can be
lifted out, you will need to jockey it around to get it out. It (they) only
fit in one way, so you can not put them back in wrong. Take care to not
damage the gasket/o-rings.

I said you can't put them in wrong, that is a bit of an error. You can put
them in crooked, and this affects the sealing when the outer ring is
replaced. You are required to put them in the proper orientation, and this
can not be screwed up.