How far ahead should I start to look for a job and how far from my ETS date should I be applying for jobs?

SPC (Join to see) do you know if either of those career choices operate on an annual cycle? I know the police departments where I live have an annual screen, test, selection and academy, swear in cycle that is 100% rigid. I would let that be your guide.

If you look in more general terms, many jobs will either be immediate advertise, interview, hire. Others may take weeks or months. The federal process is excruciatingly drawn out, unless they are DA Security Guards or Police. You'll potentially interview and be selected, then the qualification process slows it down....but you'll know something.

Easier to get in with your local or state police. Apply for both. Get in, get trained and if you still want the feds, reapply with experience

As a mechanic plenty of companies will hire you. Feel free to contact me for advice.