After receiving help, I realized that the switches were just faulty and my wiring is correct. I did also consult with an electrician who also told me that 1 in 4 of these switches can be dead on arrival. In my case, 3 of the 3 were dead.
For some more additional information on the dead switches:
- Measuring with a multimeter of traveler wire to ground.
- Pressing "off" on auxiliary brings 120V to 95V
- Pressing "on" on auxiliary brings 120V to 105V
My guess here that the internal wiring of the primary switch was fried and could not interpret these signals, which was my issue.
I'd 100% recommend turning off the power as if you send a 120V through the traveler wire in any way to the primary or the auxiliary switches, you will absolutely fry these switches.
Buying another one of these pairs and wiring them up properly did the trick.
Smart switches are not equal partners like old style 3-way switches. They are "master" and "remote".
This model of smart switch is a "master" and requires certain models of "remote" which require "neutral" (white wire) to be present in both switch boxes. That is not always so, as the electrical code only recently started requiring it.
So I'd first check the other box - if there's no neutral in it, you cannot wire a remote (though wireless options may exist). Useless old work can be dangerous, so tidy up by removing the 3-way switch, wire-nut the common to one of the messengers (trial and error will reveal which), cap the other one off, and put a blank wall plate over the hole.
If a white wire is already wired to a terminal on the old 3-way switch, bad news - that is NOT a neutral, but one of the messengers (the two inter-switch wires). Before the code change, they often used common 14/2 Romex for messenger, and one of the wires is white. They're supposed to paint or tape it.
If there is a neutral in both boxes, you can wire a remote. First, figure out which box is upstream (closest to the service panel aka breaker box). It will contain a wire that is always hot - regardless of the position of any switch.
Then review the diagram (which you already linked) showing you the wiring scheme for whichever remote you bought. You will need to re-use both of the old messenger wires.
Best Answer
Yes, try another three-way lamp.
Three-way lamps have two filaments. One on for low, the other on for medium,and both on for high.
The screwshell is the neutral and the center button and outer ring are energized together for high. If you have a voltage tester, with the lamp switch on high, you can carefully test from the center button to the outer shell. And then test from the ring to the outer shell. If you get 120 volts both times the switch is good. If not replace the switch.
If the switch is good it must be a bad lamp.
Good luck and stay safe!