If pressing on the plate stops the noise, I would be most focused on the power transformer hardware and/or the ground post nuts.
If this is just a little noise while the preamp warms up, I wouldn't be too concerned about it.
Both the EF86s and 6922 can be microphonic depending on the tube itself. I have found that sometimes the springs in the tube shields help reduce microphony, and sometimes pull them out and using just the shield can help too.