I see the sender as a resistor type, but there have been arguements from some people that swear up & down that there is NO way that a single wire carrying a varying resistance signal can work......They say that it MUST have reference voltage...which it does not in this case. If there is a voltage wire to that coil, its very well hidden.

Look at the thing...there is only one wire from the coil. The other wires all go to the pump.
If i remember right, you should be able to get a reading by working the float thru its range with a digital meter connected to the wire from the coil and ground on the tubes. These often fail due to crud build-up inside the coil. Its a simple hard plate coil, not wire wraps but plates that the contact sweeps across to find its resistance value. I have opened them before and cleaned them, but you have to be VERY careful with the small metal tabs on the coil housing. If they break off, its tough to secure the housing again. The contact is pretty fragile as well.
If opening the coil does not sound like a do-able project, I have also used a mild acid to wash out the coil and dissolve the rust/crud inside. Thats a risk, but it has worked for me.
If there is a signal but inconsistant or wrong, many folks get results from adding Techron fuel system cleaner to thier gas and allowing that to clean the sender as fuel is used. That may take several tanks of treatment if its going to work at all.