Nice work! Looks great! Congratulations on the success of your first TV project. There will be many more to come, I'm sure
With that set - does it have an aluminized picture tube? If not, it uses an ion trap. A misadjusted ion trap will result in a dim picture, even on a good tube. Basically.... the early picture tube coatings weren't too sturdy. The electron gun will, as a result of operation, emit ions. These ions are "heavier" than electrons, and if allowed to hit the phosphor coating, will wear a hole in it - resulting in a dark spot. So, to avoid this, they simply aimed the electron gun downward a bit. This way, the ions would go harmlessly into the bell of the tube, not the screen. But, then again, so do the electrons. But wait! Electrons can be redirected by a magnet. Heavier ions can't (at least not as easily). So, by using an ion trap magnet, they could bend the electrons back where they needed to be, and leave the ions to fall to the bottom. Later tubes came out with a aluminized screen, that was impervious to the ions, eliminating the need for this system entirely.
On your other Admiral - how weak did the tube test? You can get a watchable picture on even a very weak tube. Another "trick" to bring back a weak tube is to run it for a while, on just slightly higher filament voltage. Stay away from the "rejuvinate" function on the tester except for a last resort. Sometimes, a tube that's been sitting forever will come back after even just running in the set at normal voltage for a while. Something to do with the cathode coating. So, if the tube is in the red, run it at say, 7 or 8 volts (assuming a standard 6.3v filament) for a couple hours. Come back and switch it back to the normal voltage, let it run for a minute, and check the emissions, and do a life test. You might be suprised.
I have an Admiral (one of those bakelite console-ettes) with a 14" rectangular tube. When I got it, it had a brightner on it, and had a G1 to cathode short. With the tube tester, I was able to blow out the short (using remove shorts), and bring the tube back into the green by running it hot and using "clean and balance" on the tester. It's definitely watchable now. A bit dim, but watchable.
-Ian