The 63 Spridgets use a dual oil pressure and water temperature gauge. Both gauges should work off the "Bourdon Tube" methodology. That is, a fluid, in this case Oil for oil pressure and likely alcohol in the water temperature sensing bulb is used to create the needle movement by un-winding/straightening out a coil. The needle movement reflects the amount the coil un-winds and that unwinding has a range usually defined by the gauge design. Pressure and temperature will be proportional to the amounts the coils un-wind. The maximum movement on these dual gauges is about 180 degrees. The typical "cheapy" american gauge has a needle movement closer to 90 degrees, maybe a little more, while the good "Racing" type gauges go 270 degrees or even more.
So now to the question of how to fix it. The line from the sensing bulb may be kinked. It happens sometimes and you should trace the wound-wire protected sensing line back to the gauge and see if there is a kink in the line. Later gauges may have a black PVC or other thermo-plastic covering. Gently straighten it and see if that fixes it. If not, then the needle movement in the gauge may be stuck. Tap on the gauge with the engine warm and if you can remove it and get to the back where an opening might be, spray a little WD-40 in the back.
And if none of this works, then it is time for a gauge replacement. Either a stock type replacement or an after market. I have also greatly simplified the exact operation of a Bourdon Tube instrument by leaving out some of the construction details, but my description is correct in laymen's terms.
So, there may not be a typical electric sensor unit like in later 1500 Midgets.
Good Luck and HTH,
Mike