Very strange, not something I've ever heard of.
Having a read of the manual
http://hondafitjazz.com/manual3/index.html - apparently the Jazz has a Guage Control Module. The manual says:
" Gauge Control Module Self-diagnostic Function
NOTE: Before doing the self-diagnostic function, make sure the No. 1 (10 A) and the No. 22 (7.5 A) fuse in the under-dash fuse/relay box are OK.
The gauge control module has a self-diagnostic function which consists of the following checks:
The beeper drive circuit check.
The indicator drive circuit check.
The switch input test.
The LCD segment check.
The gauges drive circuit check (Tachometer, Fuel gauge, Speedometer).
The communication line check (of the body-controller area network (B-CAN) communication line and the fast-controller area network (F-CAN) communication line between the gauges)."
Not sure if that is of any help, but it does tell you which fuses to check.
You can find the Gauges section of the manual in the 'Body' section.
Other ideas: Diagnostic tool to scan for fault codes. Check battery earth strap is clean. Check battery terminals are fitted properly. Ask around for a decent local auto electrician.
HTH