This is one of the earliest references I have found to Running W.
Book was originally written circa 1750, and has been translated in to modern language...and had several possible updates, so not certain if the Running w is from the original, but
Horse Hoeing Husbandry
- Jethro Tull
You can read the entire book, as it is one of many 'full view' books available on google.
Horse and cattle training begins page 540.
As a side note to my research, the running w appears to be more utilized as an 'emergency brake' and particularly in training driving horses that bolt in the 1800's - most horses were trained to both ride and drive as needed.
When horses were replaced with automobiles, the tool fell out of common use until the cinema revived it in exciting movie horse falls. This was outlawed in 1940.
About 1970, there was a resurgence of interest in and use of the running w as a training tool in the western disciplines that spread to others.
Some consider it mainstream, others damaging.