Earliest National Hawaiian Electric steel

[pete1951]

I would expect the first small movement of the tone control to reduce volume a little and increase high treble a little, then the resistance take gain away and it becomes a sort of volume control. This is not wired as any tone control I have ever seen.
Most passive tone controls a a ‘bleed’ to earth and use a much larger value cap, .02 perhaps the most popular. Here are a few ways to wire a tone control, but your .001 will only remove the very high frequencies

[zero]

The .001 caps are a custom add that some people on use to keep some treble when you turn down the volume down some. You normally loose some of that Hi End without it, but you certainly don't need it. It's used by many who play Teles. You would still need a normal .05 cap in order for your tone control to work. The wiring on this should be like any guitar with one pickup (Vol & Tone control)and no selector switch.

[zero]

This is probably of more help, the original wiring on mine. The 2 wires on the right hand pot (that go out of the picture) are going to the jack.

[walter]

It's aliiiiive!  I went with this basic circuit diagram, and replaced the pots and cap (used a .05mfd, may change to .01).  Until an original horseshoe magnet pickup falls from the sky, this is what I'll be using.
Green leads are ground.  Center lug on the vol pot is output, and on the tone pot it's a bleed to ground for killing off treble.