Although you've already found the problem (well done), here are a couple of options for people with similar problems in the future:
Dedicated milliohm meter
A special kind of meter could have been used, but not many people have one - a milliohm meter. These are capable of measuring resistance with much greater sensitivity than typical multimeters.
Starting the measuring at one end of the "shorted" tracks and moving towards the other end, the measured resistance would have steadily decreased as the milliohm meter probes got closer to the location of the short between two tracks. This would tell you that you were getting physically closer to the short.
Continuing moving in the same direction along the tracks, the resistance would eventually then started to increase, which would tell you that you have now passed the physical location of the short. You're looking for the lowest resistance reading, to tell you that you are closest to the physical location of the short.
After removing one short, you would need to repeat the process in case there were multiple shorts between the same two tracks (as there were on your board).
Home-made milliohm meter
Another approach may be possible in your situation of a "bare" board (i.e. no components) but only if you have a variable current, current-limited power supply (e.g. a typical bench supply) and a multimeter with millivolt sensitivity. This becomes a home-made milliohm meter (not very accurate, but as I explain below, that doesn't matter in your case).
You would connect the power supply between the two "shorted" tracks, but not with the intent to burn out the short. The current is intended to cause enough of a voltage drop across even low value resistances, to have a measurable voltage drop on a good multimeter e.g. in the millivolt range.
So with the power supply set to current-limiting at say 1A († see below), you use the millivolt range of the multimeter, moving the probes along the two shorted tracks, looking for the point of lowest voltage. By Ohm's law, the point of lowest voltage, with a fixed current from the power supply, would also be the point of lowest resistance i.e. you're probes are closest to the short.
Depending on the accuracy of the current limiting from your power supply, the millivolt reading on your multimeter might not be able to be accurately converted into milliohms, but for finding a short you don't care about the absolute reading. As described above, you only care about the relative changes which occur as you move the probes along the tracks i.e. is the reading getting higher (you're moving away from the short), or is it getting lower (you're moving towards the short).
(†) As kindly pointed out by glen_geek in a comment, there is a risk with this technique that if (a) the "short" is formed with a weak-enough material, and (b) the test current is high enough to "blow out the short", then this process of trying to find the short, might remove (or partially remove) it. That prevents you actually finding it, or assessing whether it may reform in future.
Therefore it would make sense to minimise this risk, by starting with the lowest current that still allows a difference in the voltage drop to be measured along the "shorted" tracks.