Build-up on stylus - any new cures?

I have used the "Magic Eraser" (up & down as noromance & joenies mention) for years & it has worked well keeping the stylus clean. Surprisingly effective in fact... Not sure how well it will work with a stylus that has "build up" on it already, but it's worth trying. 

I use Magic Eraser and I carefully drag it from back to front. Have not had an issue in 3-4 years of doing this. However! I'm using an inexpensive Ortofon 2M Red or Blue stylus, so not as concerned about an expensive mistake.

When the stylus gets dirty, I add a few drops of 91% alcohol to the ME. That generally takes care of it. Agree with @slaw keep records clean; less gunk and your stylus will last longer.

Thanks, I actually have a bottle of that exact stuff (at least it was 91% a couple of years ago, and I have used it regularly. Whatever is stuck on their seems impervious to alcohol, though, so I'm exploring other options. I appreciate your response.

OK, for everyone that offered practical ideas for a solution, thank you! I appreciate that. My problem is somewhere in the mechanical-chemical range and pragmatic ideas are welcome.

For the various people that assumed that I don't clean my records, I actually never play one I haven't cleaned unless I cut the shrink wrap right beforehand. And sometimes I clean even new records first.

The cantilever tip around the diamond looks like a snowball with just the tip of the diamond peaking through. Dipping it into ME's (my usual cleaning method) with alcohol, or water, or even vinegar (why not?) were all equally ineffective. An Audio-Technica tacky thing was ineffective, as was a Discwasher stylus brush I got in the 1970s, both dry and with alcohol on it.

Going forward I will explore solvents and possibly ultrasonic cleaning, perhaps with that Flux HiFi gadget. Fortunately I also have the JICO replacement for the original VN-35E stylus (not SAS). It will work until I fix the SAS.