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I am planning to travel to Mexico by crossing a land border from the United States. I am a Turkish citizen so I need to register to the Electronic Authorization System. I've been having problems with finding proper English sources.

First of all is this the form that I am supposed to fill? https://www.inm.gob.mx/sae/publico/en/solicitud.html

If so is it possible to use the authorization to cross a land border or do I have to be flying to get there as wikipedia seems to suggest?

You do not need to fill out the EAS form if you enter Mexico by land.

(You also do not need to fill out the EAS form if you have a valid US visa and enter Mexico by air, but the way Timatic displays this information is confusing, so if you fly to Mexico an airline check-in agent may get confused and think that you need the EAS.)

From Mexico INM:

Si eres ruso, turco o ucraniano y planeas viajar a México por avión, obtén la autorización electrónica para ingresar como Visitante sin permiso para realizar actividades remuneradas (Turismo y Negocios), sin la necesidad de tramitar una visa mexicana.

Recuerda que si eres de esas nacionalidades y cuentas con una visa vigente en Estados Unidos, Japón, Gran Bretaña, Espacio Schengen y Canadá o eres residente permanente en esos países, también podrás ingresar al país sin necesidad de visa mexicana o de esta autorización electrónica (SAE).

Which roughly machine translates to:

If you are Russian, Turkish or Ukrainian and plan to travel to Mexico by plane, obtain electronic authorization to enter as a visitor without permission to engage in work (Tourism and Business), without the need to process a Mexican visa.

Remember that if you are one of these nationalities and have a valid visa for the United States, Japan, Britain, Schengen Area and Canada or are permanently resident in these countries, you can also enter the country without a Mexican visa or this electronic authorization (SAE).

As Dorothy noted in another answer, you do need the FMM which you can obtain online in advance, or on arrival at the border. If you choose not to get one in advance, be aware that Mexico does not stop 100% of incoming travelers at the border (yet, but they are planning to do so in the near future); you'll need to stop and go into the immigration office at the border crossing yourself. In both cases you have to stop at the border and pay the MXN 390 (about USD 21 today) fee, but filling out the form online saves a few minutes of filling out the paper form in the office.

The Instituto Nacional de Migracion [MX], as translated, explains that, if you enter Mexico by land through the northern border, it's done easily by obtaining the Multiple Migratory Form Electronics Terrestrial (FMME-T).

The FMME-T applies exclusively for you [to access] Mexico by land, by the states of Baja California, Sonora, Chihuahua, Coahuila, Nuevo Leon and Tamaulipas.

The next page contains the Forma Migratoria Múltiple (FMM), the form you need to complete. Select EN for English, then By Land, for the terms, to which, at the bottom, you must agree before the form you need to complete will appear.

After contacting the Mexican consulate I was told that as a US visa holder I do not need additional documents to get into Mexico.

Their exact response was

If you have a multiple entre visa to Canada or USA visa you don’t need visa to enter in Mexico

As advised, I went to the land border from US without any additional documents other than my passport and was allowed to pass through without any issue.

Though based on Michael Hampton's answer it is possible that I was just lucky. The consulate did not answer my additional questions about FMM and I was not stopped at the border so forgetting what Michael Hampton's answer stated, I just moved on. This did not cause any problems on re-entry to the United States