I hadn't seen this until now
I would think it unlikely you have an instrument failure
Your understanding of how it works is essentially correct except in the power for the signals is NOT common to the brake and horn (as indeed it is on the classics/roadster) -
The most common issue associated with the turn signals is in the signals' sockets themselves, very poor piece of hardware - VERY easy for the terminals to either short to ground or NOT to the bulb itself.
Fact that the dash dims probably means its looking at a short - the instrument panel I believe has protected solid-state outputs so does not 'fry' but protects itself
I would look to the sockets as the primary source of the issue.