I doubt that there would be much in the way of ferrous debris that would be attracted by a magnet, nor would that explain why such debris would deposit on the stylus and cantilever which are NOT ferrous. Nor would this explain why the condition is particular to use of gel-type stylus cleaner and not with other cleaners. This appears to be some kind of chemical deposit, and one that probably changes in property when exposed to the temperature and pressure of the stylus tracking the groove (it gets burned on in the process).
I have been practicing what is recommended by Wally Tools independent of their recommendation--mostly dry brushing to remove gross deposits, with very occasional wet cleaning with a stylus cleaner like LAST. This has worked for me. I don't see much crap building up on the stylus.