Hello again Stirling
Actually you do have a shorted tube! You make one! Testing for shorts is only a matter of proving continuity between each of the elements in the tube itself. And your tube tester does not care whether the short is internal in the tube or external. For certain. shorts take place internally. So make your own externally shorted tube. Take a single strand from number 18 or 20 stranded hook-up wire and wrap one end around the Plate pin, and the other around the cathode pin of the tube being tested. Wrap them tightly on both ends. Snip away the excess, so that those ends cannot touch the chassis of the tester or the rivets. Push the wire as close to the base of the tube as possible. You now have a shorted tube that your tube tester should detect. Go ahead, put the tube into your tester. If the tester detects this short, it probably means that there has nothing wrong with the tester at all. You can try this on two or three tubes. Whenever testing for shorts ALWAYS do the short test first. Whenever a short shows on any tube tester, stop all other testing right away, go no further. If you fail to do this you could possibly damage the tester itself. The instructions that come with some/if not all tube testers, will usually tell you this. You now know you have a bad tube. Get rid of it! If this does not work you will also know that there is still something else wrong with the tube tester.
Lots of Luck