You are going to have to pull the valve cover and see if it’s bent push rod or a bad lifter.
Bear with me here I know you don’t have solenoids.
Oiling on these G3s goes like this, Oil from the filter heads to the main galley, it feeds both the crank and Cam bears from there. There are 4 passages that head up to the heads from the main galley, each one of those passages has a branch that goes to a lifter valley , the lifter valley is divided up into 4 sperate sections.
When the solenoid is active it pushes a plunger down and blocks the oil from the head passages, at this point the lifters are only feed oil from the pushrods. Oil travels down the pushrod and bleeds out the BIG hole in the MDS lifter, allowing the lifter to collapse under the Valve spring pressure
When the lifters are getting oil feed from both sources there is enough pressure to over come the valve spring that is trying to collapse the MDS lifter.
With the Plugs installed the lifters get oil from both sources.

Now there could be MDS lifter in this engine and at idle the oil pressure is low enough now that it has some mile on it that the lifters are not “pumped” up at start.


But either way I hate being the bearer of bad news..it’ go to be opened up.