I'm ex-Aussie Air Force and I worked on Hornets for a few years.
We'd sometimes get a few FCS BLINs on startup and there's a few different extra tests that you can advise the pilot to do to help clear/isolate the fault. There's separate manuals for the FCS and Fault Isolation, that's when you'd use your BLINs. When I was running the flight line desk and launching jets it was procedure to have these 2 manuals opened and ready to access quickly.
As for the FCS exerciser, we would always try to fault find a jet with FCS problems as soon as possible after it had shut down. That way the FCS and Hyd fluid is still warm. The FCS exerciser was used if you had a cold jet and you needed to get everything warmed up to operating temperatures.
You could always expect FCS faults after the pilots had been doing BFM lol.