That is very thorough of you to check by rotating. Good call.

Removing the pump only gives you more ease/ freedom to move the chain through the full cycle when there is no other means of tension. That, or just bear in mind that for every full turn of the crank, the chain is going to experience some inconsistent advancing into the timing cavity.

If you have record of the chain being replaced, perhaps the vacuum pump (VP) has already been replaced too? If you see screws holding the plate on the front of the VP, it is most likely a replacement. I would not waste my time pulling it just to inspect it at this point, if that is the case.