To test this you will need a test light or DC voltmeter set to read 12 volts.
The first thing you need to check is the 25A park lamp fuse in the right rear junction block. I believe that's under the hood. Duplicate the condition, and probe the back side of the fuse. The voltage should be steady. If not then the problem is inside the junction block.
If the voltage is steady which I suspect it will be. You will need to gain access to the light switch wiring and the lamp control module which will be near the switch. There will be an orange/black, gray/black and two brown wires going to the module. this is where I think you are going to find your problem.
Duplicate the condition, check voltage at the org/blk wire. This is the input and should be steady. Now check voltage at the brown wires and find out which one is hot. I believe you find that this one flickers in sync with the lights. Next back-probe the other brown wire and gry/blk at the connector and connect jumper wires to good ground. This should turn the lights on but they will still flicker. If so, replace the module.
If your test results are different, let me know what you find and we can go from there
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