None wrote:
I just got my B&K 747 tube tester back from professional
calibration and service at CTech Electronics, and I'm now very
careful in how I use it, so as not to damage anything like I
aparently did before.

It is very hard to damage a tube tester... but an interelectrode
short can do the trick. Usually the meters have a diode in parallel
with their movement to limit current to a safe value.

My question is this: I now hit the 'shorts' button first thing
after the filament is lit. If it lights, I pull the tube and do NOT
hit the 'test' button.

That is always a good idea.

But is there ever a circumstance where a 'good' tube will cause
the shorts light to light? I ask because I had some 6146s a while
ago that would light the 'shorts' light up, but tested far into the
'good' range scale.

Yes, many tubes have intentional shorts that can show up on some of
the test positions. They should be mentioned on the tube chart.
If you check your tube tester manual, it may have a table that shows
what the different positions on the shorts switch test for.

For instance, on Hickok, position 1 is heater-cathode shorts...

-Chuck