Bouncing fuel gauge hand is not an issue, I would say, it is just the way it works. Later the tube-type fuel sender were introduced and those were indicating fuel level in more "civilized" manner.
I am not sure the presence of vent lines nipples is the best way to determine the type of tank you have. Do you have 65L tank and vertical spare wheel or 82L tank and horizontal spare wheel. For 1964 230SL you had originally 65L tank and vertical spare wheel, so unless someone re-built the trunk floor and moved the spare wheel, you have the 65L tank, not a 82L 230/250/280SL tank. The tank change took place in November 65 for 230SL and then this tank stayed till the end of W113.
The fuel sender and gauge set (yes, when you change one, you have to change the other) took place at chassis around 042 07XXXX for manual and 13xxx for automatic.
If you have 65L tank, you should have the early type of fuel sender.
The accuracy of reading largely depends on quality of electric connections - at the sender and through all the wiring all the way to the gauge. This I would check first.
Lots of information here:
https://www.sl113.org/wiki/Fuel/SenderUnitConsider full membership - it is all there.