If you want to soak a rod, try bear oil, lard, or raccoon oil. Raccoon oil is probably the best. The old timers said if you get one drop of it on a buffalo hide, it will eventually completely soak the hide. All will completely saturate the wood. Just wipe them down with a heavy layer, and leave them in the sun. Repeat until they soak up no more oil. Another good penetrator is automatic transmission fluid. Kerosene evaporates in a short time.
If you're going the route of petrol soaks, and like the idea of ATF, but not the red dye, use PSF. The red dye is simply to help sort out leaks in vehicles equipped with more than one hydraulic system.
I think somebuddy did a "study" and found that soaking didn't help with flexibility or breakage.
Myself is of the theory that FLEX is the last thing you want to encourage in a rod because flex will cause the rod to bear against the lands of your rifling-which could lead to wearing out a bbl and not at the muzzle end. That being said I believe that there's a lot of flexing going on anyway, and is why I try to keep my packin' stick wiped clean and free of excess grit and funk (to be perfectly untechnical about it).
I like mine scraped and hit with 220 if needed, but to maintain most the "character" of scraping. I forgot how I finished the last one, probably just finishing oils/varnish and zero stain or petrol.