I have attempted to take those Smiths BT 3331/02 fuel tank sending units apart to see "what makes them tick". I can get everything apart except the "axle" thru the case. The float & rod are one end of the axle & the arm that sweeps the coil is on the other end. That entire assembly (case, coil, axle arm & float) needs to be grounded for the sender to work. It appears as the years go by, corrosion or "crud" get between the axle & the case, causing it to lose continuity at certain spots as it swings thru its arc. That would cause the gauge needle to bounce. Since I can't remove the axle, I can't clean it up. I am able to fix it on the bench with a set of alligator clips. One successful method that I have heard of (not tried) is to solder a 24ga copper wire from the top solder joint on the arm to the case, thus providing continuity thru the arc without depending on the "axle"
That being said, New Old Stock Locators sells a correct and reliable fuel tank sender for TR3s.
Frank