Bike #1 has bar end shifters, bike #2 has little bull horn (really more calf horn) ends.
I got a piece of microphone flex from a musical supply company called Sweetwater and round the end fitting off (the spring steel flex just laughed at my hacksaw, it tickled). Then I epoxied the end into a little block of wood and screwed (bike #1, or glued bike #2) a mirror to the wood. A hose clamp holds the flex to the handlebar.
I wanted the mirror to always be with the bike. A side benefit has been that the mirror is very robust and has survived falls and railroad baggage handlers without incident (now I've probably jinxed them).