You want to wire GE 15086 timer in place of 3-way switch.
You do not have correct timer for the job.
GE 15071, 15086, 15065, 15066 series in-wall timers are for single-pole only.
Open following link to see GE timers and list of timers & manuals for 3-way switching.
Timers made for 3-way are for indoor use only and not cold weather applications. This is because these timers use a battery or rechargeable battery that will not perform long-term when exposed to cold temperatures.
Wiring for 3-way timers requires slightly different wiring at remaining 3-way switch. In other words, the timer replaces one 3-way switch, and the other 3-way remains, but wiring is different on remaining switch.
Look at manual carefully.
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