(Thanks to TB for the write-up)
Your battery doesn't have to be "dead" to consider a replacement. If your clock is not keeping accurate time, perhaps it's a time to replace the battery. The effective life of the clock battery is 2 - 3 years.
Battery part number: Renata 386 / Duracell D386 / Energizer 386 / Maxcell SR43W or you can also order via Scooterwest (1.55 V). Check the battery that is being replaced (upon removal) as well as the replacement battery (prior to install).
However the entire process (narrative and pics) is captured below in three parts:
GT/GTS: Headset Cover Removal
In the pic below, the arrows indicate four (4) screws that need to be removed. Be careful removing these screws...place a towel over any open cavity and you may want to use a magnetic screw driver or screwdriver with retaining clip. You're not done yet.
You will also need to: (1) unscrew the speedometer cable nut then (2) unscrew the bolt that holds the headset cover (with instrument panel) to the steering column and (3) cut to cable tie that holds the electric wire bundle to the steering column. Once this is done you can pop the headset cover off and then unplug the two electric connectors to the instrument panel as well as the connectors on the left and right side of headset cover. You should now have the headset cover (with instrument panel) removed and place in on a worktable to replace the battery. I recommend having it on a table...you want a stable platform to complete the battery replacement.
Carefully remove four (4) screws. Cover any open cavity with towel.
Screwdriver with retaining clip...you can use magnetic.
Speedometer cable nut...unfasten.
Unfasten this bolt...carefully...do not drop...cover open cavity with towel.
Cut this cable tie to release electrical bundle.
Plugs behind instrument panel...unplug.
Plugs...headlight, horn and turn signal...upplug. On replug give a shot of WD40.
Plug...front brake switch connector...unplug. On replug give a shot of WD40.
An inverted cup / cap covering the battery compartment...remove. Next, using a slotted screwdriver remove the plastic lock washer (push down lightly and turn counterclockwise). Next, gentle pick up and remove the spring washer. There's the battery...which is friction fit in place by two tabs...carefully remove the battery...don't damage the tabs.
Once to battery is removed...check out the charge of the "bad" battery...if the charge is good the problem could be the clock itself. Replace battery (clean off contact surface before install) and washers and cap.
Turn it over and it should be working!
Battery compartment cap / cover.
Plastic slotted washer.
Spring loaded washer.
There it is!...the battery. Remember to test charge of battery to insure the clock is not damaged.
The three components that need to go back in correct order after battery is switched out. Make sure to clean surface contacts of new batter before replacing.
2005 GT200 DASH CLOCK
Make sure you got the two dots ":" in between the hour and second digits blinking or you haven't set the clock and it won't "run".
Reassemble and you're done!
It works! Go to Owner's Manual or link to set clock.