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I don't know if this is true for the '76's, but my '78 Toro has one of these, and the mirror/thermometer is all one unit. The thermometer is not mounted separately to a standard mirror. Rather, the thermometer is part of the base. If you want one of these, you might have to find the whole mirror.
Here's a close-up of the thermometer option from the '76 Olds brochure. Looks like it's part of the mirror base. But more importantly, the brochure states that the thermometer is illuminated when the headlights are on, and it can be dimmed like the dash and dome lights by rotating the headlight switch. If your car didn't originally come with a thermometer, it wouldn't have the wiring for the light, I wouldn't think, not that you need it.
Interestingly, on my car, the outdoor thermometer is not illuminated. I wonder why Olds dropped that feature.
Thank you for the info, my 76 is not illuminated and maybe I got lucky as the thermometer came out of the mirror quite easily, I think the glue had deteriorated. Mine looks good but is reading 100 f at 60 ambient I will see if it can be calibrated.
Thanks again.
Bill