71 Demon 340, 3 speed or 4

Not true. My 68 340 S ,owned it since 4/74 never had one.

Then it was equipped with an Inland shifter, as most earlier '68s were.
The Inlands had a pull handle that had to be pulled to engage reverse.

The reverse light was used on the Hurst shifters so you had warning of when you were in reverse, since the Hursts didn't use an interlock to get into reverse.

By that reasoning, I am technically correct in stating that '68 an up used dash-mounted reverse lights. :D

To add more confusion to the mix, there were actually 2 versions of the Hurst shifter handle used, one was the traditional "block letter" stamping of the name "Hurst", the other was a "standard letter", like this type you are reading.
With the Inland shifter, that makes a total of 3 different handle possibilities for non-console cars for '68 and 3 more for consoles.

That's just the possibilities for A bodies.

Mark.