OK.......... I tried a buncha' stuff and it all got in the way.
I soon hate stuff that gets in the way because it's a recipe for getting hurt.
BAD.
So I set my lathe up with a wooden "door" that I swing around when stuff is sticking out of the tailstock. The door latches with a drop hook, crude but effective, if one a' the barnapes comes careering around the corner looking over his shoulder to catch a flying flock........... he'll just bounce off the "door." On this door I hang a rag to catch the gunk I pump/blow/splatter of boring and reaming and cleaning.
Now, I'm still not happy because I "could" still get my arm or other appendage into the hole betwixt the door and get sucked in. (well, OK, the only "other appendage" that would reach would be my LEG, and I'd hafta' be doin' the serious hokey pokey but hey, I'm a Safety Geek)....So what I do is, I wrap tape around the sticking-out screwheads. Put the lathe in free-wheel and spin a couple wraps of tape over the screws so's it looks like a square wagon wheel.
Makes me feel good.
Good is good.
al