What Snyper said.
If you want to measure because you lack the transfer punches or a lathe to make them on, you can get a conical tip
centerline attachment for the caliper for as little as $22, currently. Assuming the threads are not all the way to the top of the hole, that will work.
If the threads are all the way to the top of the hole, the top turn can bias a conical tip to the side. Same with a conical tip center finder. In that instance, take a set of number drills and find the largest size that still slips inside the thread all the way to the bottom. You use a second drill that same size for the second hole. Measure between the drills sticking up in the holes by measuring the outside space between them and also the inside space between them, and then average the result. Do it a number of times, using the smallest inside and largest outside numbers you get, as any error in jaw perpendicularity to the centerline between the drills will make the inside number larger and the outside number smaller.
My guess, though, with the 0.628" result you have now is that the actual spacing intended was 0.625", an even 5/8 of an inch. The 0.003" is a not-unacceptable cumulative tolerance error for holes to mount something like a scope ring. Also, it is easy for the eyes to be fooled about the exact location of the hole center by the top thread causing and minor optical illusion. It is also easy for calipers to be off a couple of thousandths in awkward measurements. I don't think I've ever owned a pair with inside jaws ground to perfect precision. I take the measurement, lock the jaws at that number, then measure their actual spacing with an OD thimble micrometer. The micrometer giving 0.002" difference from what the caliber readout says is not uncommon on inside jaws checked this way. Same for locking the micrometer at a fixed value and applying the jaws to measure the distance between its anvil and spindle nose.