I wouldn’t use self drilling drywall anchors if I didn’t know what I was drilling into. If it’s lath and plaster, or fiberboard or hardboard (you said there are holes???), you’ll run into problems. Use a tiny drill to drill a pilot hole. Be slow and gentle so you can feel what you're drilling into. If you hit a wood lath or a joist, screw a sufficiently long screw directly into the pilot hole and through the lath or into the joist. That (getting a good bite on a wood lath) will be at least as strong as a drywall anchor in drywall.
If you don’t hit a wood lath (you go between them, or the ceiling is not a lath and plaster ceiling) then drill the hole larger and use a good plastic anchor that’s not specific to drywall.
Re toggle bolts -- I also don't like those when I don't know what I'm drilling into. If you drill between laths and there is an excess of plaster pushed up that gap, you'll end up with a mess.