Other people do a decent job of explaining repair of the Smiths electric tachometers, so I don't feel the need to repeat it all here, but I will give you the links to the other web pages. The first one appears to be a copy of parts of the page above, with some later model information deleted, keeping the parts that pertain more to the early models used in the MG's, and adding some additional notes.
http://www.classictiger.com/techtips/motach.html

This page is for Sunbeam Alpine, including later negative ground tachs (convertible either positive or negative). It is more detailed in the repairs, including recommending replacement of more parts to restore better accuracy (as original).
http://sunbeamalpine.org/wp-content/uploads/2017/10/alpine_tach_repair_rev5.pdf

( Click for larger pictures. )

The important part in these links will be the small electrical schematic depicting the relatively simple internal workings of the electric tach. There is also a parts list for the electrical parts, in case any of those parts may need to be replaced. It is common for the electrolytic capacitor to crap out with age, and replacing that part may get a defunct tach working again.