Electro viscous fan perhaps?
Do you recall hearing the engine fan more than usual? By that I mean, the fan remains coupled to the engine rather than reverting to a sort of free wheeling state during normal operation.
I ask that as when I was having starting problems, (no real display of trouble lights or nasty messages, just clicking sounds and no start), part of the fix was to replace the electro viscous fan. (The main problem was eventually resolved by replacing the starting motor that did not yield any specific error codes.)
The electric clutch within the viscous fan takes its instructions from the engine computer rather than just sensing engine heat of the lack of it, was not alway de-clutching - at least that was what some of the dealer error codes suggested and also my ears. The reason I mention this is that there is an argument that says the engine computer will disallow an engine start if it thinks the engine cooling system will not work.
All your codes suggest a brake light circuit problem however you have installed a new switch and generally a switch problem does not inhibit engine starting - just maybe the air suspension or high speed vehicle operation.
Hence I bring up the matter of the engine cooling fan and if it sounds odd.