That is great info. So what you are doing is closing the relay yourself rather then the coil side of the relay where it energizes when power is applied to it and it pulls the contact closed.
This means that highlighted wire is not supplying voltage. So either the alarm relay has failed or the ignition lock switch (on manual transmissions) has failed or the BCM is not grounding the alarm relay.
Let's go to the ignition switch and test for voltage coming in. If you have it coming in on the green wire then you can just the switch and the engine should start. This proves the switch is the issue.
Let's start with this and go from there.
Let me know what questions you have.
Images (Click to enlarge)
Thursday, February 25th, 2021 AT 6:40 PM