I want a programmable timer that can, eg, switch on a single phase electric motor for 10 seconds every hour. It may be 9 secs or 11 secs.

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You have 220Volts (same as 240V), then that circuit does not need a neutral.
All household single phase voltage requires two wires to complete the circuit.
With 120V, you have 1 hot wire and 1 neutral wire.
With 240, you have 2 hot wires, and these hot wires are called 'out of phase' since each comes from separate side of breaker box.
Notice that your 220V 10-2 wire goes back to a double breaker. This double breaker snaps over two different busbars. The breaker pulls 2 out of phase 120Volt lines, and when testing voltage across those two out of phase 120V wires, you get 240V potential.
The ground wire is redundant safety in both 120 or 240 Volt circuits, and is not necessary for either 120 or 240 to operate.
http://waterheatertimer.org/240-v-water-heater-circuit.html#120-240

1. Press PROG
2. Press up/down arrows to select the programme you wish to set (16 spaces are available)
3. Press SET
4. Press up/down arrows to set the hour at which watering is to start
5. Press SET to store the hour
6. Press up/down arrows to set the minutes at which watering is to start
7. Press SET to store the minutes
8. Press up/down arrows to set the number of hours over which watering is to take place (0-9)
9. Press SET to store the hours
10. Press up/down arrows to set the number of minutes over which watering is to take place (0-59)
11. Press SET to store the minutes
12. Press up/down arrows to select which days of the week watering is to take place (2nd means every second day, 3rd means every third day). When the required day of week is displayed press SET to store that day. The next day of the week will then be displayed and Set can again be used to store that day. Carry on throughout the seven days of the week as required.
13. Press the clock symbol to store the programme.

Leviton 6651 Manual.
http://waterheatertimer.org/pdf/Leviton-6651-manual.pdf
Timer requires a battery which should be replaced each 12 to 18 months.
Timer replaces single-pole or 3-way switch, and does not need a separate neutral wire.
Timer is for incandescent lights only.
500 Watt capacity
Push the door for manual override to reverse program that is in effect.

The 14 hour timing period is represented by 24 dip switches.
Each dip switch is positioned for ON or OFF.

Click the dip switch right or left
Start at the bottom
For example: ON for 3 hours, OFF for 4 hours, ON again for 3 hours:
Click dip switches 1 thru 3 to ON position, 4 thru 7 to OFF position, 8 thru 10 to ON position
ON position is to the right.
OFF position is to the left.

At the end of the 14 hour program, the timer turns lights OFF until the original start time is reached after 24 hours.
Timer will operate like this while in AUTO mode, until function switch is moved from AUTO to MAN or OFF modes.
Function switch is located at very bottom of timer door.
To activate program (on first day), function switch is set to OFF position for 2 seconds, and then move function switch to AUTO mode, and programming cycle begins.

If the electrical 120 volt source is single phase, the only way to run this motor is with a single phase to three phase converter. Best to sell the three phase motor and obtain a similar horsepower 120 volt single-phase capacitor-start motor (1750 RPM) for the compressor. You would also require a 3-phase pressure switch for use with the 3-phase motor. Hope this helps!

A search of prince channel site for 735 timer sent me to the 740 timer >> their other models wer 755 and 840

Here's the prince castle page:
http://www.princecastle.com/products/timers_740series_single-display.asp

Here's the 2 instruction guides:
740 horizontal
740 vertical

The timer is a multi-channel countdown timer which means it can control multiple electrical devices separate from each other
Set the french fry cooker to tun on for 5 minutes
Set the dryer to come on for 10 minutes
Set the blower to come on for 1 hour
Set each item for different lengths of time
The item with least amount of time left shows on the screen

To program timer
Press and hold Prince Castle logo for six seconds
Time displays will change from " ----" to "PROG"

Press timer channel to be programmed
LED indicator light will turn yellow and beep will sound

Current programmed time will display (for example it might show 5 minutes 20 seconds)
Time value will indicate either H:M (hours-minutes) or M:S (minutes-second)

Press SCAN/UP arrow or SCAN/DOWN arrow to change program time
These arrows are located next to Prince Castle logo

If you want H:M instead of M:S, then press and hold SCAN/UP button
When display reaches 59:59 it will automatically change to 1:00 Hour
LED indicator light switches from M:S to H:M

Now you programmed first channel, click next channel and repeat steps above

To FINISH programming, press Prince Castle logo for a moment, and programs are saved

It is indeed possible to use ONE Phase to run a motor, You simply use One Phase and Neutral. BUT ONLY if the 3 phase is Double, more or less, the required usage Voltage, EG: 440 3 phase, will be OK, for 220 single phase, . But 220 3 Phase,will not run a 240. single Phase. So in your case is suspect not, it really will do no harm to try though. it just wouldn't work, if not enough "juice", be careful.
http://en.wikipedia.org/wiki/Three-phase_electric_power

Short in the motor - It may be salvagable but not likely. Try a local electric motor repair shop but call first for labor charges. Some don't work on 'small' single phase motors. If it is not the winding that is bad expect to pay about $100 to fix it, assuming it can be fixed. If not, a new one is probably $150 or more depending on horsepower.