Mechanical timing is different from ignition timing... You're adjusting the ignition timing not the mechanical. See the MKIII FAQ section.
Code 51 is not a typical fault error and will NEVER cause a CEL, it doesn't even remain in the ECU once the problem is remedied. I've already stated what it means and the only thing it really affects is transitioning into idle. There are two different circuits in the TPS. The IDL switch circuit (which is all that that error is for) and the TPS circuit which helps the ECU determine how the throttle is being applied. If the resistance is out of spec it may cause some issue with smooth handling but its affect on emissions should be extremely minimal. It is a wear component and should probably be replaced every 75K to 100K miles.
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