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:
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