Shouldn't be too tough to cut a gasket out of sheet rubber.  The black EPDM they use for roofing would probably be a good choice.  It will hold up well outside and should be around 3/32" thick.  You should be able to buy a small roll for seams, or if you know a roofer they probably can just give you some scrap. 

Try "Fatties Mirrors"; https://www.haganauto.com/category_s/197.htm
Maybe they can help.
I have some 1/16" and 1/8" rubber gasket material that I plan to cut for the mirror gasket, but I do not know the material type, or manufacturer.  (I've had them for years)

I got my 3" x 9"  sheet from Amazon in 1 day cost was zero ( I stole my wife's bonus points).

I cut them out using both an exacto knife, and scissors.  They did not turn out as perfect as I wanted, but they aren't too darn shabby!  I do think 3/32 was a solid choice not to thin and not too thick.   Mainly posting this now in case this comes up again and someone else needs to make gaskets.
https://www.amazon.com/gp/aw/d/B0CJYN9331?psc=1&ref=ppx_pop_mob_b_asin_title

If the picture posting gets fixed, I will snap a pic.

If the picture posting option gets fixed, the button leads to a poll for some reason,   I will post what I did, and what I made.  I don't know any other way to post it.

Greg B wrote:

If the picture posting option gets fixed, the button leads to a poll for some reason, I will post what I did, and what I made. I don't know any other way to post it.

I use Imgur - you post the photos there and use the link provided to post here.  If you want, you can email the images to me (rextherocket@yahoo.com), I'll put them on Imgur and post them here. 

Even though the mirrors carry the same part #, the bases are slightly different, most likely from different molds.   So each gasket is different because it's cut to its respective base.   They were probably churning these out in multiple molds in four different factories back in the day.

Cut with exacto knife out of 3/32 sheet, and used a hole punch to cut 1/8 screw holes.