Need wiring diagram for installing a photoelectric switch to turn lights on at dusk and off at dawn. 3 wires, red, white and black.

GE 15086 will not work for 3-way.
There are several timers that do... keep in mind that 3-way timers replace 1 or the other switch, but not both... and the remianing switch must be rewired slightly depending on which 3-way switch is replaced. Sounds confusing, but copy following links for exact wiring diagrams for the GE 15312 timer, and Intermatic ST01c 3-way timers: Easiest to wire is ST01C since it is battery-powered.
Another thing to remember, is that when the remaining switch is flipped in a 3-way timer circuit, it just reverses the timer programming, so dawn-dusk would become dusk-dawn etc.
These timers offer astronomic dawn-dusk function or 7-day programming.
http://waterheatertimer.org/How-to-wire-GE-15312-timer.html
http://waterheatertimer.org/ST01C-program.html#3-way
Gene
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The unit has motion-sensor/ photo eye capability built in.
There are no replacement parts for this type of device. Or long-term warranty.
The solution that comes to mind immediately is to rewire unit to by-pass the sensor, then install astro dawn-dusk wall timer in place of light switch.
http://waterheatertimer.org/How-to-wire-timers.html
Or install round box extension on the wall box, and wire up separate photo-eye mounted in the box extension.
http://waterheatertimer.org/How-to-install-and-troubleshoot-photo-eye.html

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

If lights blink on-off, then red wire is connected where blue wire should be.
Red wire should be capped, and not used when timer is used for single pole operation.
OR connect red wire and blue wire together if you want Dawn-to-dusk operation instead of dusk-to-dawn
Open following link and scroll down to bottom for wiring diagrams.
http://waterheatertimer.org/ST01C-program.html

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

Need more information.
Project is not clearly defined.
Add a comment with clear description of each wire and what Load is being controlled.
Why are you using a 4-way switch? Are you controlling 240Volt circuit?

Photoelectric switch usually has red, black, white wires, and usually replaces a single pole switch but can also be used to control 240Volt circuit in some wiring diagrams.
http://waterheatertimer.org/images/Wire-photo-eye-125.jpg

4-way switch has 4 screw terminals and is generally not used to replace a single-pole photoelectric eye, but can be used to control 240Volt circuit in some wiring diagrams, so I'm not sure what you are doing.
http://waterheatertimer.org/images/Typical-3-Way-switches-450.jpg

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The dawn to dusk feature is activated by photoelectric eye that senses when it gets dark.
If you put timer in a dark room, it will turn ON ... let's say to operate Christmas tree after you leave a room for the evening.
But if room stays dark, the timer will not sense when to turn off unless you also set timer to turn off 1-9 hours after ON.
That being said, a Christmas tree might make too much light for the timer's photoelectric eye.
Make sure photoelectric eye is turned away from direct light.

1) Put black tape over photoelectric eye on timer.
Photo-eye is small round eyeball that bulges out.
See of lights stay on.

2) Turn timer away from source of light so photoelectric eye does not pick up feedback from lights.

It sounds like photo eye is receiving enough light that it turns off, 'thinking' it's dawn.
And then when lights are off, photo eye 'thinks' it's dark again, so lights come back on.

Let me know if this is the answer, because it's Christmas season, and folks have been asking about blinking outdoor timers. And then you're en-route to become fixya expert and boost your GNP by 3 cents an answer.

first when installing a photocell there should be a black wire a red wire and a white wire, black goes to power coming from house, red is connected to black wire in post to light, white goes to the neutral wire coming from home, if you have any other wires you wired it wrong

one of the white wires has power on it constantly....that wire connects to the black wire of the leviton.......the other white wire which has no power to it is going to whatever needs power so that wire connects to the red wire of the leviton....the green wire connects to the metal box where your mounting the leviton.

Connectthe SUPPLY wire (Black) to the Photoelectric Black. ALL of the white wires - to lights and from supply and on PE - connect together
Redfrom PE goes to all light fixture black lines