My dimmer switch clicked nicely, but failed a continuity test.
I began investigating by taking off the button -cap, which was not necessary in my case. Only after did I find I could carefully pry out the terminals as an assembly, even though it looks like pot metal, which I thought would crack away. This may not be possible for all dimmer makes.

The terminals and the toggle have fairly robust contacts
, (picture 1))and these were dark and greasy. There was a lot of lube on the toggle, and it probably evaporated somewhat over 55 years, and settled on contacts. The toggle is plastic, and not broken up, the return springs on the cap-to-togglepin assembly were fine (picture 2). All I did was clean all contacts, relube toggle, reinstall cap and put terminal assembly back in with a little RTV, and it works
That's all there is in the dimmer, so don't be afraid to dig in.
The only reason you might have to remove the button;-cap would be if the cap doesn't spring back. To remove, drill out both indentations on cap, but remove as little metal as possible, because you will need to re-indent the cap directly over the 2grooves in the dimmer, see pic 3. A small screwdriver or punch will indent cap. A wood block under the cap supports the cap in a level position while you drill and re-indent it.
I now have an original dimmer, made in USAa.