Walker SST, like any of these products, is simply a suspension of silver particles, in an organic vehicle. Whatever is used in these products, canola oil, or otherwise, will dry out over time if it is in the open air.
The conductivity of silver is what it is, it's the highest conductivity material you can find.. Whether it is in the form that the manufacturer sold it (dried powder), or in the finished product that is SST, etc., you cannot make it less conductive. Silver can oxidize, but even silver oxide is quite conductive - but let's presume that it has not oxidized.
In order to have continuity, you need to form a continuous chain of silver particles that the electrons (electricity) can flow through. Just like wire, if you cut a wire, no matter how good or bad the conductive material is, it will not pass the continuity test. You are essentially making a wire when you do the test you did - think of it in these terms. ANY voids whatsoever in your film (line) will result in the electrons not being able to flow, and you have the situation you are in now.
Personally, if you are using bare wood, that would be one of the more difficult materials to find success with. The reason being you are dealing with a very non - uniform surface. The odds of being able to form a contiguous silver film on any such surface is quite low. Try a perfectly smooth non - conductive material, such as glass or acrylic (plexiglass), and try again.
Follow Lloyd's recommendations. If he tells you that canola oil is the appropriate thinner, you can bank on it. His goal is for the material not just to work, but for it to make a profound improvement for you. Just be sure to not add to much, as again, your goal is to wind up with a film where you have no voids whatsoever - contiguous silver particles, from one end to the other. The more silver you have in the paste, the easier that is. The more oil, or anything else, the more difficult it becomes.