3 way timer switch

I am trying to add a digital timer switch to a 3 way configuration. I got the switch to work with one issue, it only works if the 1st switch in the circuit is in the on position. Please note that the other switch is a standard on off switch. If I turn the 1st switch off, I cannot turn the lights on from the digital timer. If I have it on, then the timer works perfectly to control the lights. To make matters a little more interesting, I do not have the more common configuration for 3 way switches. I have the configuration in the attached diagram where one switch flows through the second junction box to the lights. The digital timer is in the #2 position in the diagram below.

Can anyone help me to get this working correctly? Do I just need a second digital switch or am I SOL to get the timer to work with this setup?

All switches in the circuit must be designed for 3-way circuitry - you can't use a simple on/off switch in a 3-way circuit. The timer you have may or may not be able to work in a 3-way circuit. Without knowing what you have, there's no way to tell you how to make it work.

If your wiring at the matches the illustration a digital timer may not work since there is no neutral at either switch location.