2005 5.4 with cam phaser lockout installed

Did you try a new sending unit? cheapest thing to try,the old one might be lazy. For the rough idle, did you check for a vacuum leak?

does it idle rough when you go in reverse or as you slow down for a stop sign or red light?

It idles rough at and idle and when you stop at a light then shows low oil pressure but only for a second then bounces back up. I have not tried either of those. It only has 105,xxx km on it

So you don't want to resolve the problem because it has only 105,000 km on it????

A bad idle control valve could be the problem.

It sounds like you need a new oil pump, or oil pressure sensor. Part of the reason the Cam Phasers go out is a weak oil pump. When you replace it, go with the upgraded pump that has a stiffer metal back as that will fix the issue.

Oil pump

I’ve fixed a lot of these for this exact problem. First you should check your oil pressure hot, load the engine in gear then let off the throttle quick, if it drops to 5 or less check the crankshaft endplay, the two piece thrust can stack on top of rack other and cause a large oil pressure loss that will lead to engine failure. Putting a high volume oil pump on willjust mask the problem for a while. The other probable cause is the cam bearing surface damaged/scored. I have replaced heads on trucks with less than 20k on them

Have you tried a different volume of oil? Are you using a 5w20 . and when you put the eliminator in how bad was the ticking before because you can have other damaged parts from the phasers like the timing chain you should always change new tensioners , the spacers and chain just for the gp. Most likely its a timing issue and fixing that your pressure will return to normal depending on further parts that may be effected from the phasers.