I am not really sure why they stay in. They just do. It is kind of like using staples instead of thumb tacks on a bulletin board. Both the staples and thumb tacks stay in. If they come out, try putting them in at opposing angles.
Perhaps a Camry visor of the same year will fit and would be more available at the boneyards. VIP may even be able to order one from their catalog for a small fraction of the dealer price. I’ve done that before.
If you decide to be really frugal and try velcro, there are picture hanging systems that use a shallow-looped vekcro with a removable goop (gelatinous? elastometric? I’m unsure…) that should work. I just bout some a few months ago at the WalMart and hung some photos on a textured surface. They worked great.
You can adhere the velcro to fabric with cyanoacrylate (crazy glue).
I like the idea of checking with an upholstery shop. At the very least, they can remove the fabric cover so you can see the mechanism and determine if you can repair it or not. The mirror should drop down after removing a couple of screws, then there should be an electrical connector for the mirror lights tucked up there. Once out, they should be easy to work on.
I’ve found that used car managers at dealerships are a good source of information for reasonably priced upholstery shops. These managers routinely send cars to these shops for upholstery work before the cars go on the lot. These used car managers know which upholstery shops do good work for the best price and may even have you tell the upholstery shop that you were sent by the used car manager of the dealership.
Any reason you cant glue the velcro to the fabric? If you use staples won’t they bend against the metal of the car top that is above the headliner? Cheap people don’t mind a few tiny dents in the car top do they? I’m cheap and it wouldn’t bother me at all. I once hand painted a truck with outdoor house paint just to keep it from rusting out. What the hey.
One reason would be that if it didn’t work, it would create visible damage.
I don’t think regular office staples are strong enough to dent your car body. I also don’t recommend using staples that are long enough to penetrate the material and scratch the metal.
If you use a combination of glue and staples, the staples will get a little glue on them as they go in.