When a customer's weld specifications called out "no more than 0.010" of undercut" and began rejecting our parts based on that specification, we asked them "How are you measuring it?" because like engraved text, something could be .010 wide and .009 deep and there isn't much in the way of metrology devices that would allow someone to measure it. Their reply was "If we can see it it's that deep."
So I made a device that would hold a 0.001" button indicator in a block, and in the block pivoted an arm which had a very fine probing point on one end, and a rest for the indicator button on the other end. They accepted that device as being the last word on how deep undercut was.
The only way I can think of to actually measure depth of engraving is in a similar fashion. A test indicator with a probe fine enough to actually get past the wall of the engraving.
And not worth your time. The fingernail test is best, IMO.