Where to find intermediate gear -about 1/2 " in diameter.

Are you sure that you put the pins on right? They have little projections on the bottom that turn the timer on/off as the cam moves through its 24 hour rotation. The little gear in the back is connected to the motor and because it is spinning that tells you that the motor is definitely good.

1) Clock motor is worn out, or gears are dirty:
http://waterheatertimer.org/Malibu-power-pack-stopped-working.html

2) Take apart clock motor and add white grease to gears
Set override to ON, and plug timer into cheap wall timer.
Take advantage of 5-year warranty.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

1) If you have programmable timer, then it would require 24 ON and 24 OFF settings, with down-to-the minute programming.
1 ON for each hour.
1 OFF for each hour.
Following link shows Grasslin 50-60 Hz 230Volt din rail timer with 50 memory slots. 16 amp at 230 volts
http://waterheatertimer.org/pdf/talento_371_372_371_mini_plus_data.pdf

2) If you have 24 hour mechanical timer with dial, it would need 24 ON trippers and 24 off trippers with down-to-the minute schedule.
No timer has that capability.

3) There is C8800 series cycle timer. 120-240Volt 60Hz for US market. 20 amp at 120volts, or 20 amp at 240Volt. Chose 1 hour cycle, then insert 100 trippers and leave 20 blank spaces.
http://waterheatertimer.org/pdf/027-C8800-sprinkler-cycle-timer.pdf

4) There are percentage cycle timers.
For example CT2000. Rated 120Volts 60 Hz for US market.
http://waterheatertimer.org/pdf/CT2000_sell-sheet-with-wiring.pdf
Select 1 hour cycle, and 16% or 84% percentage to choose ON or OFF

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Question posted under analog power strip.
Analog timer has small clock motor.
When the plastic motor gears wear down, the clock begins to make noise.
Might not hear the noise when TV is turned on.

To get analog timers to last longer, be sure to keep timer in dust-free environment so nothing clogs the gears.
I don't know how to take apart this timer without breaking it.
http://waterheatertimer.org/GE-timers-and-manuals.html#striptimer

New GE timer at Amazon $10.46
http://www.amazon.com/57698-24-Hour-Power-Strip-Timer/dp/B00067OOFY/ref=sr_1_1?ie=UTF8&qid=1292413124&sr=8-1
Heavier duty Woods timer at Amazon $19.62
http://www.amazon.com/Woods-22575-24-Hour-Power-8-Outlets/dp/B002L706K4
Buy Utilitec power strip timer locally at Lowes and save shipping.
Buy GE at Home Depot and save shipping.

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And take advantage of fixya expert assistance live.
For a price, expert works with you while you work on timer or any do-it-yourself project.
Fixya is always less expensive than a service call.

Question is not clear, timer is not identified.
Add a comment with in-focus photo of timer posted on flickr.

Minimum on-off time for digital timers is usually 1 minute.

Minimum on-off time for plug-in-type 24-hour analog timers is 1/4 hour or 1/2 hour depending on width of tripper-pin-segment.
Minimum on-off time for plug-in-type 7-day analog timer is usually 3 hours.
Plug-in vacation timers are set for random on-off and cannot be set.
Minimum on-off time for box timers with 24 hour dial and wide tripper is 1 to 1-1/2 hours
Minimum on-off time for box timers with 24 hour dial and narrow tripper is 1/4 hour.
Minimum on-off time for box timers with 7-day dial is usually 3 hours

Open following link for information how to set analog timers
http://waterheatertimer.org/How-to-set-timers.html

STARTING SYSTEM Starter REMOVAL & INSTALLATION Fig. 1: Disconnect the wiring from the starter motor
Fig. 2: After unbolting the starter, remove it from the vehicle
In 1978, a gear reduction starter was introduced on some Canadian and United States models. The differences between the gear reduction and conventional starters are: the gear reduction starter has a set of ratio reduction gears while the conventional starter does not. The extra gears on the gear reduction starter make the starter pinion gear turn at about half the speed of the starter, giving the starter twice the turning power of a conventional starter.

1. Disconnect the negative battery cable from the battery.
2. Tag and disconnect the wiring at the starter, taking note of the positions for correct reinstallation.
3. Remove the bolts attaching the starter to the engine and remove the starter from the vehicle.
4. Install the starter in the reverse order of removal.

Your timer could be broken.

But let's review.
Override set atTimer on > correct
When override is moved other direction, then lamp turns on.
Lamp fixture is turned on
Bulb is good
Receptacle has power
You tied timer on different lamp at a different receptacle.
Dial rotates with passing time, which indicates that clock motor is functioning
Dial does not get stuck during rotation, and makes complete 24 hour circuit in 24 hours, indicating that clock motor is not weak.

Segments up or down for timer functions >> here's what to do: pull up some segments. Manually rotate timer dial clockwise.
The lights will turn on-off as you rotate dial manually.
That will confirm if up or down is correct position of segments.

If everything above checks out, timer should work.
If timer is defective, exchange for another one.

I test these timers and 4-6% arrive defective. Most last one or two seasons and then they quit.
Some last years.
But timers today are priced low enough.

You need a programmable interval timer.

http://waterheatertimer.org/Intermatic-timers-and-manuals.html#ET70
Intermatic and Tork make digital timers with interval settings that can be set for specific short-duration with 1 minute minimum.
(Or set to pulse bell ringing with 1-127 seconds.
10 minutes is 600 seconds)
For example ET70115 single-channel timer.
The timer would be set for 24-hour operation, and then programmed for Pulse, and then set timer with 24 programs, with 1 program for each hour.

Mechanical cycle timers from Intermatic:
http://waterheatertimer.org/Intermatic-timers-and-manuals.html#cycle
1) Talento 1 hour cycle timer/ each tripper represents 1.25 minutes
2) Model C8835/ each tripper represents 15 seconds.
To operate these timers certain hours of the day, add another timer in-line.
The in-line timer could be digital, but remember digital timers are not protected from power surge and tend to have more problems, and do not have replaceable clock motors and trippers.

You simply need a pulley 3.5 times the diameter of the Drive. Say 1750RPM reduced to say 500RPM. So Divide 1750 x 500 = 3.5. /10 It is simply a "Ratio" Therefore we need a reduction of 0.35:1 or 1:.0.35 meaning every full revolution on the "Drive" means .35 Revolution on the "Driven". So if your Drive pulley is say 5" Diam, you will need the Driven to be 17.5". So the Drive make 1750 Revolutions, the Driven makes 500. Use whatever actual figure you like, simply "Scale" up or down. Hope this helps.

Hi The product you have given has Built-in flash with Auto, Forced on, Red-eye on, and forced off (Red-eye reduction On or Off).
There is a 1 1/8" diameter lens with a built-in lens cover that automatically opens and closes when the on/off button is pressed. Above the lens is the viewfinder window, flash and tiny (almost unnoticeable) microphone. There is also a small circle that has three functions: the autofocus assist beam, red-eye reduction lamp, self-timer lamp. A wrist strap comes with the camera and attaches through a slot on the front of the camera near the side.
To the right of those buttons is the four-way controller, used for menu navigation as well as:

• Up - Metering (Evaluative, center-weighted, spot)
• Down - Drive (Single-shot, continuous, self-timer)
• Left - Focus (Auto, macro, infinity)
• Right - Flash (Auto w/redeye reduction, auto, flash on w/redeye reduction, flash on, flash off)