Clare, Xeno.... and anyone else who has actually mounted tires at home...
this is a question simply to hone my skills, based on your experience.

Did you ever have a batch that just wouldn't seal after the final bead?
o How did you prevent that from happening?
o If it did happen, why did it happen, and, more importantly,
o What TOOL do I need to get to solve this problem without helpers?

As you are well aware, everyone around me burns through tires due to the
artificially high steering-induced positive camber causing camber scrub on
the inside edge of the front wheels due to steep long windy hilly mountain
one-lane asphalt roads:
https://i.postimg.cc/FzGQY92V/mount51.jpg

And, as you are aware, I patchplug my own tires, as needed, since they get
punctured usually about once or twice per set per lifetime of that set.
https://i.postimg.cc/GpYwkPW2/mount52.jpg

I buy whatever tools I need to mount tires at home, such as this HF bead
breaker:
https://i.postimg.cc/wxDM6L39/mount47.jpg
which, I admit, sucks - particularly on the larger stiffer light truck
tires, but, with a few slight modifications (such as the long board you see
in this picture to "extend" the base - it works well enough such that in
just a minute or two all the beads I've ever attempted have been broken:
https://i.postimg.cc/FKfFwJ25/mount48.jpg

In the past, you helped me with the various little-known tricks of the
trade, such as the use of dish detergent and water to lubricate the bead
https://i.postimg.cc/KvZGxWd5/mount49.jpg

And you helped me understand the 'drop center' where there are about a
dozen such tricks that are needed to more easily break and mount the six
beads overall for each tire, before you seal it with the air pressure.
https://i.postimg.cc/ZqyZwzdJ/mount50.jpg

One indispensable trick Clare patiently explained is the clear distinction
between the "yellow" dot and "red" dot for steel wheels which have long ago
lost their match-mounting marks:
https://i.postimg.cc/J0p91pkT/mount54.jpg

And, another bit of useful advice that the experts know is which tire
valves are best, where I'm slowly using up my supply of the rubber ones so
that I can go to the bolt on ones in the future exclusively:
https://i.postimg.cc/rmk6g0T9/mount53.jpg

Over time, taking in all this advice, I've successfully mounted & balanced
almost two score tires at home, as witnessed by this pile being just the
recent trash that I need to drop off at Costco at $1 per tire, plus tax.
https://i.postimg.cc/0NGXktgp/mount59.jpg

Where I must say, they balanced BEAUTIFULLY (better than ever before!):
https://i.postimg.cc/28JK2bFB/mount58.jpg

And yet - even after about 40 tires under my belt in the past few years, I
_still_ occasionally get a stubber set of tires - like this last batch -
which just wouldn't seat for the final pressurization stage after all six
beads were mounted.
https://i.postimg.cc/4yxSFpSp/mount57.jpg

The problem was, without TWO HELPERS!, I couldn't seal the final bead for
the life of me to pressurize the tire - which was a new problem for me.
https://i.postimg.cc/J4d9vdm0/mount55.jpg

Everything else was easy - but I couldn't get the air to stay inside!
https://i.postimg.cc/wvVrVw06/mount56.jpg

Literally, I had to use 2 additional helpers just to squish the tire
enough that I could get the bead to hold air for that critical first few
seconds (and yes, the schrader valve was removed where I used the same
equipment I've always used on these same sized passenger truck tires).

The only thing I did differently with this set of passenger truck tires was
that they were stored on their treads for about half a year, since I bought
two sets of the same tires, on sale, so I stored them.

Only after I pondered WHY was this one set so difficult to get the bead to
seat did I wonder if they're supposed to be stored 'flat' and if that made
the difference????

Did you ever have a set of tires that just wouldn't easily seal?

Two questions arise if you have experience with this specific problem.
1. What additional tools do I need to purchase?
2. What trick can I do to make it easier to seal the beads?