Pull the mirror out just a bit from the window by pushing it forward and then pull off the tape shield and press the mount into the glass. I usually use 2 layers of tape which seem to work the best. It will not vibrate or fall off.
Are your original mirrors on the car in the picture? Those look great but the a hand built mirror with what appears to be a bicycle mirror on a ball adjust adjustment epoxied to the fiberglass housing. ( had a customer send me one that fell off so I dissected it) The mirror mount system was original designed for the 2 wheeler and was most likely not intended to go 100+ MPH which is why it may not stay adjusted--IMHO