Could try the following
Let’s assume the counter top runs east west and from the front of the sink to back is north south.
The target zone is the existing circular hole in the metal flange
From underneath the sink can you measure from the center of the target zone to a reference point eg yhe outside wall of the sink. We don’t need to be accurate, but accurate enough that if we sink two random small pilot holes from the top they will go through the target zone.
Can you then drill two small vertical holes from the top and you can use the jig to make sure you are vertical.
Now go back under the sink and measure from each pilot hole north south east and west to the edge of the target zone circle.
You should have 8 measurements 4 for each hole hole one north
H1N, H1S ,H1E H1W , H2N H2S H2E H2W
Now transpose those measurements to the top of the sink ( don’t mix them up) so you make a point at distance H1N notleth of hole one etc
You now have 8 points that are on the edge of a circle.
Make a paper circle 1 1/4 in diameter with a hole at the center.
Position that so its edges touch the 8 points you have and mark the center
More pilot holes are better as it helps average out any small measurement errors and my gut says try and get them 1/3 radius off center.
You do know, don’t you, that the line between brilliance and madness is often razor thin.

Also if you can do 3 holes you can dispense with any errors on your north south east west reference by drawing a line through each pair of holes up to the target zone circumference
L1 is h1 to h2
L2 is h2 to h3
L3 is h3 to h1
Then your measurement are from H1 along L1 to the circumference
I may have over done the coffee and trying too hard to avoid actual work today.
We just had a kitchen installed and saw them drilling the holes for the same thing, fortunately they had a cardboard template in the box the sink came in for just that purpose.
I guess the OP could see if the sink manual has any of the required measurements in it if they can find it on line
Also FWIW they didn’t use water to cool but did wear some serious face masks and had a vacuum cleaner on the go. I suspect the water mentioned is more for dust suppression, very finely ground granite dust or quartz is not stuff you want in your lungs or eyes.
This. Plywood would work fine as a jig for measurement. Drill a centre hole and do as you describe
I like this idea. A small (e.g. 1/2") rare earth magnet centered in the hole on the underside should easily project its power through 3/4" of countertop. Put a little tiny rare earth magnet on the top and it ought to immediately zip to the center of its bigger brother’s field. Rotate the under-sink magnet and you ought to see the top one rotate in place.
That’s where to center the drill.
More in depth.
Use the hole saw to make a"plug", mark your centre, drill through from the bottom and do as you describe.
Once you have the centre ref, use your “plug” draw your circle with a sharpie, plug the centre hole with plumber’s putty and make a shallow ring around the space about 1" larger with plumbers’ putty or Plasticine.Add a bit of water and use your hole saw.
I think keeping a vertical hole from drilling underneath will be tough , so maybe stick the plug into the hole underneath, drill two holes vertically from the top though counter top through plug assuming we can position either enough confidence .
Move plug to the top and line up with the two holes , drill center hole from top and off you go.
That’s what I kept thinking, and – if I get the picture correctly – he’ll have to work past the sink to get to the hole he’s trying to drill.
I think the mechanics, the access, and the visibility might all be impediments – not insurmountable, necessarily, but PITAs, nonetheless.
Your quartz description make me wonder if there’s any chance a very bright light could be seen from the other side.
Just asking a question…
I’ve installed a couple of these and don’t recall the tolerances being so crucial that a pilot hole from the bottom wouldn’t work. What am I missing?
It’s actually a good question.
I just glanced at the sink earlier - it’s possible that the hole in the flange is bigger than 1 1/4" to allow for some slop. I’ll go check it later.
I think the magnet idea for locating the hole seems a very fine plan. Assuming the countertop material doesn’t contain iron compounds, 3/4" should be no problem for a pair of strong rare earth magnets and if the one on top seems to be gripping the surface material too much, a little bit of oil or soapy water should allow it to slip so it finds the centre of the field of the magnet below.
For drilling, a core bit will need to be restrained not only to keep it vertical, but to prevent it from skittering across the surface while it is initially biting in. For this, you could just drill through a piece of scrap timber, making the hole that is the same as the outside diameter of your core drill (ideally drilling this hole with a drill press to make sure it is straight.
Add a couple of thin pieces of ply at both ends of this timber scrap so it’s like a small bridge (because you want water to flow underneath), fix it down to the material in the right place using strong double sided tape, build a small dam around the whole thing using modelling clay and flood it with water, then drill down through the hole in the wood, through the stone worktop. Back the drill off every 10 seconds to allow water to run down into the cut, and if it’s a diamond cutting tool, let the weight of the drill do the cutting
Regarding the magnetic technique, there’s a decent chance that a ball bearing would suffice up top (in place of a magnet).
The ball bearing idea is ingenious, because the ball should be self-centering over the magnet.
Could you just pack a wet sponge into the hole saw and drill from the bottom? As the saw advances into the countertop, the “plug” you are sawing out would gradually advance into the saw and squeeze water out of the sponge and onto the cutting edge. BE CAREFUL: Wrap the drill so water could not get in. Have someone watch who could unplug the drill immediately if some does leak by.
On second thought, never mind using water. Too Dangerous!
Just remember the quartz dust is really bad for you. I think the long term exposure gets you all sorts of nasty health issues, so I doubt one plug drilling is a big deal, but wearing a mask and goggles is a simple safety measure.
You’re all over-complicating this.
What is the hole spacing of the sink deck holes? The norm is 4". Remove whatever is in the hole adjacent to where you want to drill. Find center of hole, measure 4" over and drill.
I did this on my quartz countertops to add a soap dispenser and dishwasher air gap, and had no problems. You may want a standard 1-1/4" hole saw to drill the plywood as diamond bits pretty much suck at drilling wood. I used a Milwaukee diamond cutter with a spring-loaded carbide center point. Don’t recall needing to use water on it.
Beowulff: Please let us know, have you tried to drill the hole?
Not yet.
The original RF switch is still working, so I’ve been able to dodge this bullet.
But, the suggestion that made the most common sense was @gotpasswords - he picked up on the obvious solution that I had missed.