[DaleHCook]

I get continuity between wires 1 and 2. Does that mean that I should solder them together and attach #3 to the larger wire with the heat shrink.

Which brand and model is this radio? It is always wise to specify the brand and model so that we can look at the service information for that set. Many of us have service info for most brands in Rider and Beitman. Some of us also have a number of factory service manuals for non-Philco radios (I have most of the factory service manuals for Zenith and RCA).

I suspect that you don't have a sufficiently sensitive ohmmeter to measure the resistance between wires 1 and 2, and don't have the instrumentation to measure the impedance between them. There are undoubtedly some turns between them, because it would be redundant and unneededly expensive to bring two leads out of the field coil if they were shorted internally.