How to mount TV in old drywall or plaster wall
If any type of drywall anchors are failing me, I immediately switch to toggle bolts. The down side being that if they also rip out they're going to pull off large sections of plaster. Finding the studs is always better.

To find a stud without a stud finder, try 3" screws every inch or so until you find one and then try measuring to help find the next, usually they're on 16" centers. If it's a small section of wall, there might just be one in the center or they might have split the difference and used two. It's also entirely possible that on a 32" wall there isn't one.

If you're willing to poke a hole, 20 little pinpricks should be no problem and if you're lucky the mount will hide them anyway.