?Setting the petcock to prime fills the carb bowls, drawing fuel from that source. The stock petcock is vaccum operated so you may leave it with the On position. Now, fuel leakage may indicate that the petcock seals or the unit itself is failing, no cause for alarm.
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Id double check that and confirm. Tearing into carbs is not always good for inexperienced people or always necessary and carb removal/installation is one of the very few 'issues' this bike has.
I would change the oil prior to even starting it because running it with any gas in the oil thins it and can cause damage to the motor.
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If you require a petcock rebuild it usually is more cost effective to source a new petcock. Previous owner of my ride installed a manual fuel shutoff for any just in case moments.?
The W is such a well engineered ride, it is a no BS no frills bike that runs like a champ if ridden consistently and complete basic recommended maintenance. We have some owners with over 100,000k on the clock still running strong.