Is there a way to determine if you have a faulty fuel sending unit or the fuel gauge without removing the sending unit?
If you unplug the sender wire the gauge should go past full, grounding the wire should make it go to empty. Check the sender with an ohmeter to see if it has any resistance.
1 Ensure that all wiring connections (both on the back of the gauge and on the sender unit) are clean, tight, and free from dirt and corrosion. 2 Turn the ignition on and off several times in succession and note if the needle moves at all. If there is no movement, check to make sure you have power. If no power, Connect a jumper wire to the ignition switch and the terminal on the back of the fuel gauge, then turn the vehicle on. If the gauge now works, replace the defective wiring between the gauge and the ignition switch. 3 Ground the gauge by clipping one end of the jumper wire onto the gauge's grounding terminal and the other end onto a clean contact point on the vehicle's frame, then turn the vehicle on. If the gauge starts working, replace the defective fuel gauge grounding wire. 4 Ground the sender unit with the jumper wire using the method described in the previous step. The sender unit can be grounded by attaching the jumper wire to the exterior of the fuel tank or the vehicle's frame. Replace the sender unit's grounding wire if the gauge begins to function. 5 Disconnect the wire that connects the fuel gauge to the sender unit, then turn the vehicle on. If the fuel gauge reads full, this indicates a problem with the sender unit. If the gauge continues to read empty, you most likely have a faulty fuel gauge that needs to be replaced.
Once I find what the problem is, can I purchase a direct replacement for either the gauge or the sending unit?
usually the sender is bad http://www.classicparts.com/1960-66-Gas-Tank-Sending-Unit/productinfo/23-527/ but test anyways...
Power probes Those things are legit, and can help you easily pin point electrical issues. IDK if it's appropriate for this specific application, but if you find yourself neck deep in wires, a Power Probe is a good thing to look into! - FNG
Until I receive my new sending unit I don't want to run out of gas. Any idea how many gallons is the tank in my 1966 C10?
about 15 but you might be able to look it up here http://www.gmheritagecenter.com/gm-heritage-archive/vehicle-information-kits.html download the file for the 66 pickup truck, and have fun reading...
Squirrel, I must be an idiot as I cant seem to find the area on the "GM heritage" site where you can look about certain years and models.