Hello and thank you for using just answer!
Whar is the code # XXXXX in the computer here and did this pop up after a repair was performed?
This will not be a cam position sensor.
The p0300-p0306 are happening because if the 1346 and 1349 codes......
If you clear the codes and then drive the car with the scan tool what code or codes pop up first here?
this must be aglitch in your scan tool then, ignore the 1346 code then.
Have you made any inspections on the timing belt yet?
Have you looked INSIDE the engine at all?
P1349 is for the variable valve timing. Basically the computer commands the camshaft to move position and it does this by means of oil pressure through the oil control valve on the front of the engine, you will see a metal line that holds the high pressure oil near the front.
This code is most commonly caused by one of 3 things here:
1- Stretched or jumped timing belt. Do be aware this is an interference motor, if the belt breaks it's game over for this engine.
2- Deposits inside the engine such as gel/sludge that restrict the oil passages and the oil control valve. Removing a valve cover to inspect the condition of the intenal engine is a good idea here.
3- Bad oil control valve or a bad vvt-i camgear actuator.
how do you find out which is the problem? can the oil control valve be diagnosed or do you just need to replace it? How would you recommend me to continue with this situation?
The really good scan tools like the $5,000 one I have from Lexus has the ability to perform an active test on the oil control valve.
Being that this issue is intermittent you may not be able to duplicate this with an active test.
I would double check the engine for deposits, do a synthetic oil change here and at least remove the oil control valve and see if it looks dirty to consider replacing it or not.
I have had a few of these with bad cam gear actuators also but that is not nearly as common as the oil control valves.