If you place a sign directly on top of another sign then there will be z-fighting at the base of the top sign's post.
Steps to Reproduce:
Summon a sign that's on top of another sign.
/fill ~ ~ ~ ~ ~1 ~ minecraft:oak_sign
Look at where the signs come in contact with one another and move your mouse cursor around slowly.
Observed Behavior:
Z-fighting can be seen when signs are placed on top of other signs.
Expected Behavior:
Z-fighting would not be able to be seen when signs are placed on top of other signs.
Confirmed.