I know this is an old thread, but I recently went through this same issue on my '99 Southwind 36Z. I have had this coach since it was new, so I can tell you both the source of the original damage and my ultimate solution.
The cause, as the author of the thread eventually learned, was wood rot. The backing plates for the Velvac mirrors are a couple layers of 1/2 inch plywood, as best I could tell after removing the mirror and probing around the holes. It was spongy and would no longer hold the large wood screws with which the heavy mirror was mounted.
In my case, the dry rot began from an unsuspected water leak around the TV antenna. Despite apparently intact caulking, water gradually worked its way into the roof structure and eventually down to the mirror mount. The roof repair is another long story, so I'll stay on subject to relate the solution to the mirror issue.
The remedy was a product I remembered from by boating days called Git-Rot. I got mine from Amazon and watched a YouTube video by a boat owner on its use. This is a penetrating two part resin that saturates the rotted wood and cures overnight, restoring its strength and integrity. I'll let the directions and videos explain the details. The only tip I'll add is to make sure the holes you drill through the fiberglass into the rotted wood to allow saturation are slanted downward so the resin does not run out and flow down the side of the coach.
The next morning, new, slightly longer and fatter stainless steel wood screws fastened the mirror solidly back on the coach. If the screws had refused to bite my fallback was going to be though bolts and fender washers on the inside of the wall, which is hidden up under the dash and out of sight. This might not be a good solution on the driver's side, but on the passenger side there was nothing to damage or interfere. Fortunately, this was not necessary because the Git-Rot did what its name implied.
5 yrs US Army, 35 yrs US Customs (retired)
RVing with DW, kids, grand-kids, and dogs since '77
'99 Southwind 36Z - Ford F53, 5 Star Tune, CHF