Absolutely mention it. Some employers like to use technician jobs as a way of vetting employees for greater responsibilities. Since you've been applying for engineering positions, clearly you're interested in moving beyond the technician position in the future. You should communicate that when interviewing for a technician position, to avoid putting yourself and your employer in an awkward position later on if they have no pathway for promotion between technician and engineer classifications/titles.
It's very common at my place of employment for students to start out in paid internships and move directly into technician classifications after graduating (doing mostly the same work). This lets them continue to apply for scientist and engineer positions, internally and/or with other employers, without a lapse in employment.
Other employers can be less comfortable with the idea of hiring a more qualified candidate into a less qualified position. Don't deceive them, you'll only make yourself miserable in the long run. Ask during your interview what sort of pathway the company or agency has for technicians to move into full engineer positions. It's a good situation for them because they can pay you a technician's wages without actually committing to promote you. It's a good situation for you because you haven't been able to find other employment, and you can keep applying for other jobs if you don't like it enough at that job to wait for an opportunity to open up.
As for where and when to mention it:
- Do put it on your resume. This is an important qualification that demonstrates your value to the employer, regardless of what position(s) they have open at the time.
- Your choice how and whether to mention it on your cover letter. I think it's more important in the cover letter to make a connection between you and the company. Communicate why you are interested in them as an employer, so they will be interested to look at your resume, which you will have attached.
Engineering Firm, Inc.
123 Fake Street
RE: [Position identifier or description]
Dear [hiring manager's name]:
I am a recent graduate of Alma Mater University in [location], seeking
employment with a [subfield or industry] engineering firm. I was
interested to read [some item related to the firm]. While at Alma
Mater University, [describe accomplishment, experience or personal
connection related to the previous item].
I've attached my resume ... (good fit, love to talk with you further, looking forward to your response, blah, blah, blah - just try to be reasonably genuine)
If you're sending the letter in response to a job announcement, be sure to mention the job (by identifier number/code if possible, by description/title otherwise) at the very beginning of the letter. There's no need to mention it again in the body of the letter. If it feels natural to do so, then do so. If not, then don't. This communicates clearly that you are responding to a specific advertisement, while sending the message that what you're really interested in is working for this company. If the only opening they have that you're qualified for is a technician position, then this is the best approach.
A good employer is not looking for someone to be a technician forever. They can always train another technician; or, if you impress them a great deal in the interview, they may invite you to interview for a better position that hasn't been announced yet.