I would verify the 'known clock issue' as xintersecty said and go from there.
You will eliminate that aspect as a possible problem, and potentially save yourself tedious wiring troubleshooting.
The clock is quite easy to take out. On my 05 hatchback the two side panels beside the radio and blower need to come off first.
You can use a plastic 'putty knife' and start at the bottom by the cup holder and start to pry it up/out.
Once the side panels are removed you will see two Phillips screws beside the radio holding the top panel.
After you remove those screws pry up the panel starting from the radio and working your way towards the clock on either side.
Once the panel is up and out, disconnect the connector to the hazard switch on the panel so it can be fully removed.
You will now have full access to the clock, two Phillips screws and a connector to take it fully out.

The intermittent operation isn't going to be a fuse problem.

Cheers