I don't know how to change timing on electric sign outdoor timer

Can you take in-focus photo of wiring diagram shown in timer manual, and attach them to comment?

1) Copy following links:
http://waterheatertimer.org/images/Wire-GM40-timer-600.jpg
http://waterheatertimer.org/Woods-timers-and-manuals.html

2) Right now, dec 2012, there is no product manual for this timer.
Thank you for including the terminal markings.

3) I assume jumpers are for changing voltage?
Please add comment and say what your product manual says about J1 J2 J3 J4 jumpers.

4) Load is water heater
Timer is clock that is set and programmmed to turn switches on-off.
NC is normally closed > when timer is OFF, NC and NC2 terminals are ON
NO is normally open > when timer is OFF, NO and NO2 terminals are OFF
When timer turns ON, then the switching reverses, and NO terminals turn ON, and NC terminals turn OFF.

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

Which timer do your have?
Not all timers work with fan motors?
Are you adding a new bath fan? Or are you installing a new timer?

What transformer what checked? A transformer is used to change voltage. For example you can plug a Malibu outdoor-light transformer into ordinary 120V outlet and the transformer changes voltage to 12 volts so you can safely operate lights stuck into the ground around bushes. Or your phone recharges using transformer that converts ordinary 120Volt into very low voltage entering your phone.
Practically every electronic device in your home has a transformer ... microwave, TV, computer ... but I don't know why a bath fan would have a transformer.
Add a comment, and I will respond.
http://waterheatertimer.org/Countdown-timer-horsepower-ratings.html
http://waterheatertimer.org/How-to-wire-timers.html

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

More information is needed about the timer.
Open following link to help identify timer:
http://waterheatertimer.org/Boxtype.html

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

Copy following link to troubleshoot Intermatic timer:
http://waterheatertimer.org/How-to-troubleshoot-Intermatic-timers.html
http://waterheatertimer.org/Intermatic-timers-and-manuals.html

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

More information is needed about timer.
Check out following options, or add a comment any time.
Adding a comment send email and I will answer.

1) Open following link for setting analog timers.
Applies to in-wall and plug-in type analog timers.
http://waterheatertimer.org/How-to-set-timers.html

2) For a programmable timer, a comment and describe timer buttons, and include if timer is in-wall or plug-in.

3) Open following link to see Intermatic, Woods, and GE timers plug-in, in-wall, and box timers, including indoor and outdoor:
http://waterheatertimer.org/Intermatic-timers-and-manuals.html
http://waterheatertimer.org/Woods-timers-and-manuals.html
http://waterheatertimer.org/GE-timers-and-manuals.html

You can do it yourself.
Anybody that knows 'hardwired' and observed timer is making humming sound can wire up a timer.
If M88T timer dial is not rotating, but power pack is making humming sound, then that says timer is receiving power but clock motor has gone bad.
There are no replacement clock motors for power packs.
http://waterheatertimer.org/Malibu-power-pack-stopped-working.html

To wire a new timer:
Click circuit breakers until the humming sound turns off.
Turn breaker back on to confirm that humming sound is associated with that breaker.
Buy a tester at local hardware and ask them how to use it.
Tester will give you assurance that power is off when connecting new timer.

Outdoors: put down dry boards to stand on, never stand on bare soil or wet/damp surface, don't touch anything metal and don't hold metal screwdriver in mouth while working on electric circuit. Wear gloves if you want. And don't sweat.
With 120volt circuit, as long as you are not grounded, which means that you are not touching soil, or anything that grounds back to soil, then you will not get electrocuted. You can get shocked only if power is still turned on at circuit breaker, and it will be surprising, but it won't kill you as long as you're not grounded. All electricity goes back into the earth to complete circuit.

Open the box where timer is hardwired.
Use tester on black wire. To confirm power is off.
Typical 120volt circuit: Black wire is Hot and carries voltage. White wire is neutral and completes the circuit back to ground. Bare copper wire is ground and serves as redundant safety.

Old 88T timer will be wired black-to-black, white-to-white, and green-to-bare copper.
Take photo of wiring to avoid confusion. Post photo on flickr and add a comment with link to photo for another pair of eyes on situation.
Cut off end of new timer wire, strip insulation with knife and attach wires same way previous timer was connected.
http://waterheatertimer.org/How-to-twist-electric-wire.html

To install ordinary 120Volt outlet so timer can plug in: Buy outlet from hardware: Black hot wire connects to brass-colored screw, white neutral wire connects to silver-colored screw, bare ground wire connects to green-colored screw.

Open following link to see basic circuits:
http://waterheatertimer.org/B220C.html
http://waterheatertimer.org/See-inside-main-breaker-box.html

This can get complicated without more information:
I don't know how much electrical knowledge you have.
I don't know if your lights are 120V, or 240volt.

Following links might help: The photo eye is probably 120Volt. The lights can be 120V or 240V.
http://waterheatertimer.org/How-to-wire-Cooper-277-pilot-light-switch.html#photo-eye
http://waterheatertimer.org/images/wire-ga-250.jpg
http://waterheatertimer.org/240-v-water-heater-circuit.html
http://waterheatertimer.org/See-inside-main-breaker-box.html

Add a comment with as much detail as possible for follow-up help

Yes 40 amp is standard, and you can use it.
Amp rating can be thought of as roadway capacity.
The higher the roadway capacity, the more cars (or electricity) can go down the road at same time.
If you have 40 amp roadway, but only use 20 amps, then it's like the highway has fewer cars. Except with electricity, the cars don't go faster, but just like a regular roadway, fewer cars means less heat and the roadway lasts longer. So you want larger amp rating.
http://waterheatertimer.org/How-to-wire-T104-Intermatic-timer.html#T101
http://waterheatertimer.org/See-inside-main-breaker-box.html

Most digital timers suggest resetting as last-step effort to restore functionality.
This particular timer is reset by removing battery.
Try removing battery again. Otherwise it seems the timer has gone bad.
HB88RC is discontinued product.
Replacement is heavy-duty Intermatic HB800RCL 2-outlet or HB800RCH 1-outlet timer.
http://www.smarthome.com/25078/Intermatic-HB800RCL-Heavy-Duty-Digital-Appliance-Timer/p.aspx
http://www.smarthome.com/48715/Intermatic-HB800RCH-Outdoor-Digital-Timer/p.aspx

Less expensive and less reliable timer Woods 59403 with 1-outlet has quite a few 'timer won't work' questions on fixya.
http://www.amazon.com/Woods-59403-Heavy-Duty-Outdoor-Digital/dp/B002KS7EOK
http://waterheatertimer.org/Woods-timers-and-manuals.html#6-24

You posted under Woods outdoor 2-outlet timer 59403:
Add a comment if this is not your timer
http://waterheatertimer.org/Woods-timers-and-manuals.html

Lets run through trouble spots others have with programmable timers:
Add a comment any time and I will help.

What we know for sure:
-Battery is working because display shows.
-Manual override works, so basic electricity is OK and light is OK

-Common programming problems:
-You set current time and it shows in display > if current time is not set or does not advance with passing time, then timer does not know when to turn on-and-off. Double check display for current day, hour, and minute.

-Each event has ON time and OFF time. So you set event1 ON and then set event1 OFF. For example some people set ON time and don't realize each ON needs corresponding OFF, or can't find how to set OFF. Trick is making sure timer display matches fig3 and fig4 shown in manual. Press PROG button until display shows 1ON for event1 ON and then press PROG button until display shows 1OFF for event1 OFF.
-To review programs and double-check, press PROG button repeatedly to scroll through programming. Check for ON and OFF days, and for overlapping on-off commands.
-Event1 ON and event1 OFF should be set for same day(s). For example event1 ON is set for Tuesday but event1 OFF is set for All-days (instead of Tuesday) will conflict and timer will not function.
-Conflicts in programming will cause problems. Conflict example: Event1 says ON 7pm OFF 9pm Tues, but event2 says opposite.
-Make schedule of on-off times before programming to avoid conflicts.

Setting Mode:
MODE is manual override button: press it to set Automatic, ON-OFF override, or Random
Press MODE button until RDN displays in upper left corner, and then press MODE one more time to enter AUTOMATIC >>> you want automatic for programming functions.

Circuit analyzer: If above items check out 100%, and timer still doesn't work, plug timer to indoor plug on another circuit (not on outdoor plug). This will check if outdoor plug has electrical problem interfering with electronics inside timer. Buy cheap plug-in circuit analyzer from Home Depot electric department and double-check circuits.

59403 manual:
http://waterheatertimer.org/pdf/Woods-59403.pdf