Ok, this kinda sums it all up.
1) Bike Bandit's schematic shows the plastic knob with screw.
2) Triumph's schematic shows the plastic knob with screw.
3) Triumph and the dealers words were;
"...Good afternoon. I went ahead and forwarded your message on to Triumph
North America. Their assessment, based on the photographs, is that the
internal part of the reset knob is broken. It has a flat edge with threads
inside of it to channel the knob, which appear to broken on yours (the
shiny portion indicates this). Their recommendation is that the
speedometer be replaced, as there is no way to fix the internal portion
(where the knob threads into). A new speedometer is $289.46 plus tax.
Please let me know if I can be of any further assistance on this matter.
--
Sincerely and respectfully,
"Sincerely and respectfully"!??? REALLY!???
How is stickin' it up my ass to the tune of $300 respectful??? lol
Does anybody really need a tripometer THAT damn bad? lol NOT ME!
Anyway, went to the hobby shop, got a 12" tube of brass for $1.75 that just fit over the remaining metal shaft, and slightly reamed out the plastic knobs hole to allow the brass tube to slip into it. Measurements showed I needed about a 2" length. It was a tight, press fit into the plastic knob, and sucked a couple drops of epoxy into the other end of the brass tube like a straw, and slipped it over the shaft, yesterday.
Today revealed a perfect fix!
Kinda pissed I'm stuck with 10" of brass tube that I don't need.

PS. I believe the speedometers are everywhere on-line for about $150