I'm not a teacher or instructor or an anything, so take my advice with a big steaming cup of FWIW:
When I want my horses to slow into a jog, I adopt an approach like this:
Someone who has a very flexible back can ride a horse like that without putting pressure on the horse's back, but I cannot. However, I find it easy to stay in the saddle. My horses then want to relieve the pressure on their backs, so they figured out pretty quick to slow into a gentle jog. Because we've done it a lot, my mare interprets my moving into that position as "Settle down, relax, give me a smooth ride and we'll both be happy". My avatar is a picture taken when I was asking for a jog, so not quite as extreme as Jack was doing in 1912.
If I want her to trot faster, I bring my legs back and start shifting my weight forward.
I can't tell you if that would work for anyone else since 95% of my riding is done on my own mare (and I'm the one who has ridden her for 99% of her riding life). A lot of what we do is stuff we've figured out together.