OP - I think you were on to something when you mentioned checking the oil pressure. The noise that we're hearing sounds almost "plastic". If you havent already I'd check down inside the front cover. Not the top one either, but the lower one. Or, just look down inside. It may be obvious what is wrong.

I say this because the impressions I get when the sound starts is that it your guides are worn and your tensioner is not doing its job fully, allowing the chain to drag over what is left of the guides.

If the engine has sat for a long period of time and you didnt flush out the old oil and add new, much like Empire mentioned with the gas, its not helping matters any. The galley that feeds the oil to the tensioner and even the cams is crazy small. Its easily clogged with sludge from old oil causing all kinds of "stuff" to go wrong.

Checking these things wont cost a lot of $ either, only your time. Just be prepare beacause what you find may end up costing you $$ to fix. But think of it as an investment in reliability.