Correct, my 09 has done it a couple of times in Jan when it was single digits.
My 05 did it for about 4 years when cold. When it began to happen a lot during the restarts, later in the day, I replaced it.
If you pull it and grease the shaft it should be good to go. do it on when it gets warmer outside.
219,000miles 5/2012 ej257 short block, 8/2011 installed VF52 turbo, @20.8psi, 280whp, 300ftlbs. CHECK your oil, these cars use it.
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