I’m not familiar with your specific sun visor, but visors on Honda Civics of that vintage would split along the top edge, allowing internal detent springs to spread and the visor to flop. The solution is to catch the problem early and hold things together with a pair of screws with low profile heads - one source is “Hillman Threaded Post with Screw Aluminum”, 5/8inch length, and they may be known by other names. There are several on-line videos detailing the procedure, search for things like “Honda Visor Repair”, and see if the design is similar to yours. I’ve repaired a few and on replacement visors install these screws proactively.
As others have advised, a dash cover may be your best bet. It wasn’t just Toyota, Subaru’s of about your vintage had the sticky dash problem as well.