Being either Residente Permanente or Residente Temporal you are not a dual citizen. You are simply a bonafied foreign resident of Mexico.
Residente Temporal can only be obtained for a maximum of four years, after which the
Mexican Government expects that you love living in Mexico and desire to become a permanent resident.
If you are retired with sufficient assets/pension income you may be eligible to go directly to Residente Permanente.
Residente Permanente never needs to be renewed. This carries all the rights of a citizen except the right to vote. It automatically comes with the right to work, all you need to do is inform immigration of your activities and register with Hacienda (the Mexican IRS) and pay your taxes on income earned in Mexico. With Residente Permanente, owning a foreign plated vehicle is not allowed.
With Residente Temporal or Tourist Visa you can own a foreign plated vehicle.
The application process for either Permanente or Temporal starts at a Mexican Embassy or Consulate outside the country of Mexico. (Usually the one closest to your home.) Once approved, you have 6 months to come to Mexico to complete the process. You will then enter Mexico with a Tourist Visa and start the completion process in the city you intend to live. (San Miguel de Allende, of course!). Once here you then have 30 days to go to immigration to complete the process. This completion process takes 4-6 weeks on average.
Note: you will apply for your resident visa outside of Mexico. When you enter you will enter on a Tourist FMM. You need to mark the boxes correctly in order to transition to your new status. Watch this closely!