Thanks for the information on the sending unit. I went ahead and ordered a new unit, which sounds like it should solve the problem. I'll keep you updated.
As for the mirror (LH side), the "mounting foot" for the one on the car (which appears original) is 4 1/2" long, the mounting foot on the replacement one made by Tex are only 3 1/4". So, the replacement would not even cover the holes where the old unit was. It is the black plastic retaining bit for the glass that has broken. The mirror housing and glass bit are in good shape.
Thanks for any further ideas or suggestions.
I had a similar issue recently and to fix it I reversed the mount then fashioned a small metal plate secured by the fixing screw so that it acted as a wedge engaging the metal brackets sloping surface in place of the broken off plastic. I suppose its a bodge but it can't be seen when the mirror is in place and its stronger than the original. Its also a good idea to keep the ball and socket lubricated so that adjustment doesn't stress the mounting.