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You said you got 12.38V at terminal 86 (with relay removed), let see if your TN/RD wire is bad or not.
This time you jump from the other end of the TN/RD wire at your range sensor without removing the range sensor (from the red arrow above) to the TN/RD wire from underneath the relay panel that you did earlier (without removing the relay), then turn your key to start.
You need the following:
Without removing the connector at the range sensor, insert into pin 12 as shown below:
Below diagram locate C171 (range sensor):
The test above is to add another wire (your jumper wire) to your existing TN/RD.
You just said you jumped from battery + to 87 please do this one more time, this time use a voltmeter at terminal 87 while doing it let see what cranking voltage you get. If you get below 9.6V you need to charge your battery before doing further test otherwise the test results are going to be inaccurate and misleading.
You said you got 12.38V at terminal 86 (with relay removed), let see if your TN/RD wire is bad or not.
This time you jump from the other end of the TN/RD wire at your range sensor without removing the range sensor (from the red arrow above) to the TN/RD wire from underneath the relay panel that you did earlier (without removing the relay), then turn your key to start.
You need the following:
Without removing the connector at the range sensor, insert into pin 12 as shown below:
Below diagram locate C171 (range sensor):
The test above is to add another wire (your jumper wire) to your existing TN/RD.
Ok I ran this test and get nothing when i turn key with jumper wire from C171 12 to TN/RD behind relay panel
Remove the jumper wire from range sensor to terminal 86 and forget the TN/RD wire for now, add a wire from battery post to terminal 30 (underneath relay panel) then turn your key to start, does it crank or not.
You just said you jumped from battery + to 87 please do this one more time, this time use a voltmeter at terminal 87 while doing it let see what cranking voltage you get. If you get below 9.6V you need to charge your battery before doing further test otherwise the test results are going to be inaccurate and misleading.
Remove the jumper wire from range sensor to terminal 86 and forget the TN/RD wire for now, add a wire from battery post to terminal 30 (underneath relay panel) then turn your key to start, does it crank or not.
You already confirmed previously at terminal 30 (LG/VT wire) with 12.56V. So tomorrow when you test this, it's to assume your relay can energize, you add a new wire (in case your LG/VT wire is bad), your jumper wire from battery 12v post to your terminal 30 from underneath the relay, and while turning your key to start and at the same time if possible, also use a voltmeter and check on your terminal 87 from underneath just to see if you get any non-zero volt.
Seriously if you have the following:
it would be much more easier to see exactly what's going on since you bench test your relay and all working fine. If you can use this relay female socket to bench test one more time and see if it works (getting voltage on terminal 87), then do the semi-bench test on your car with your relay plugs into this (as an extension), and 4 wire ends plug into your relay box, you can check for the voltage easier (getting voltage on terminal 87) from the top instead of underneath.