Long exposure timed shutter release
Though not programmable in any way, the Fujifilm USB remote release might do the job:
REMOTE RELEASE RR-80
Perfect stillness is critical for long exposure, telephoto, and
landscape photography. With this remote release, you can
prevent blurring caused by vibrations when you press the
shutter and never lose a priceless photo opportunity.
Or you might opt for a traditional threaded cable release.
Bulb mode appears to have a maximum limit of 60 minutes according to brochure:
|Valley by the light of a blue moon by cjf2|
from Down in the Valley
|Lake Erie Stone Pier by yobbyt|
from Dock or Pier
|Hong Kong by Zephyr1977|