Hopefully your testing the wiring with the relay removed from the circuit because the relay could be defective ?
Did you bench test the relay?
As a test on continuity;
Disconnect the battery and remove the AMI fuse under the dash board then connect a ohm meter lead to the AM1 pfuse input on the fuse box and the other lead of the ohm meter to pin 2 with relay removed then turn the key to crack position and observe the resistance it should be a low or zero resistance but definitely not open resistance.
If it is an open circuit work your way back.
I had one probe of the DMM in the relay junction block while checking so yes relay was removed.
I did not bench test the relay, two pins have 120 ohms, the other two are open....... which is what I would expect. Without getting trigger voltage to relay it seemed a moot point to bench test it.
AM1 fuse has voltage, pin 2 has nothing..... I think it's safe to assume there's no continuity there.
The PNP switch has voltage going in...... the reverse lights work (for what its worth) I can't back probe that connector while it's installed, nor did I want to stab 22 gauge wires. So I can't say if voltage is coming out in P or N. A connector with pigtails would be nice.
Looking at the schematic, it looks to me like it goes from the PNP swth to the ECM...... I think that's a good point for me to quit on it and send it to Toyota.
I did look on RockAuto for a PNP switch.......$316........ it's a pretty basic, standard looking switch to!