Setting azimuth by orienting the stylus in the groove so it sits squarely is different from setting azimuth electrically. You seem to know this. There are some very good papers on this subject, and reading them led me to the practice of setting azimuth by the physical method.
However, to set azimuth electrically, you will need a test LP that contains a band that encodes a single pure frequency (typically 1000Hz) in the R channel with no signal in the L channel, and then also contains a second band that encodes the same frequency in the L channel with no signal in the R channel. Shure and probably some other companies made such test LPs. Then you first calibrate your system by setting the signal strength to be equal in each channel. In other words, play the R channel band and observe the db or voltage in the R channel. Do the same with the L channel signal, and set the two to be roughly equal in db. Now play the R channel band and observe the signal strength that appears in the L channel. Then play the L channel band and observe the signal strength in the R channel. Adjust azimuth toward one of two possible goals: equal crosstalk vs lowest possible crosstalk, regardless of equalizing. There is another whole argument about which of those two goals is to be preferred, electrically speaking, because in my experience "equal" is never the same azimuth setting as "lowest". Also, keep in mind the obvious fact that you would like to insert your meter or scope as close to the cartridge output as possible. If you readout at the phono stage outputs, then you are including any inequalities between the two channels of your phono stage in the data. On the other hand, trying to read the microscopic voltages from an LOMC cartridge directly can be frustrating or impossible if you want repeatable results. It's easy with high output cartridges and good instruments.
However, to set azimuth electrically, you will need a test LP that contains a band that encodes a single pure frequency (typically 1000Hz) in the R channel with no signal in the L channel, and then also contains a second band that encodes the same frequency in the L channel with no signal in the R channel. Shure and probably some other companies made such test LPs. Then you first calibrate your system by setting the signal strength to be equal in each channel. In other words, play the R channel band and observe the db or voltage in the R channel. Do the same with the L channel signal, and set the two to be roughly equal in db. Now play the R channel band and observe the signal strength that appears in the L channel. Then play the L channel band and observe the signal strength in the R channel. Adjust azimuth toward one of two possible goals: equal crosstalk vs lowest possible crosstalk, regardless of equalizing. There is another whole argument about which of those two goals is to be preferred, electrically speaking, because in my experience "equal" is never the same azimuth setting as "lowest". Also, keep in mind the obvious fact that you would like to insert your meter or scope as close to the cartridge output as possible. If you readout at the phono stage outputs, then you are including any inequalities between the two channels of your phono stage in the data. On the other hand, trying to read the microscopic voltages from an LOMC cartridge directly can be frustrating or impossible if you want repeatable results. It's easy with high output cartridges and good instruments.