I'd never used a tension gauge, so I looked at videos by two pros. Both showed how gauges worked, and both said you don't need one. The said they may use a gauge after they adjust by sound, to check. They said within 20% is fine.
Gauges did not appear until about 1960, after more than a century of bicycling. One would have been devised sooner if anyone had seen a need. It reminds me of the torque wrench, a simple tool where a pointer shows how far the handle flexes, yet none was devised until the 1930s, perhaps a century after steel machine screws became common. By 1930, cars and other machines were built on assembly lines. A new employee might not know how to torque a fastener by feel, and many were being screwed into sheet steel or soft alloys. On an assembly line, an employee could do a lot of damage by over- or undertightening. A torque wrench could provide a number for him to learn to torque by feel.
About 1960, the market for 15 mph utility bikes was drying up. People were buying 30 mph "racers"with thin spokes and light rims. I think thinner spokes would stretch elastically more than thicker ones and therefore needed a preload to keep the rim from moving laterally. At the same time, overtightening could damage light hubs, spokes, and rims. A mechanic who tensioned a lightweight wheel too tightly or loosely could cause trouble for a lot customers and perhaps damage the manufacturer's reputation. I think the tension gauge was devised for a mechanic to document that his tension was within the manufacturer's numbers.
HarryS noted that said that when there are gears, the rear rim must be offset from the hub. The rim of my Abound isn't offset because the hub is 2" from the chain stay on one side due to the cassette and 2" from the other side due to the disk brake. My front rim has spokes on one side 3mm shorter than the other. The contact patch must be centered on the steering axis, especially when the brake is applied, but the hub is offset 12mm to make room for the disk and caliper. Laterally, the nipples are 18mm from the disk-side flange and 42 from the other. If a balance in the lateral component of spoke tensions held the rim in place, tension on the shorter spokes would have to be twice that on the longer ones. Dinging, that would be like the difference between C and F sharp.
I heard no such difference when I tapped spokes the first time around, and I tuned them the same. A deck of cards can be used as a feeler gauge with increments of about 0.25mm. My rim is offset by 1 card, or about 0.25mm. That proves HarryS is right. With ebike spokes at least, tensions are similar even when a rim is offset. Length is what counts.