Thank you?

Real Intel work is done with boots on the ground. Maps, terrain analysis, tracking message traffic and targeting in your AO. MI units is where soldiers go to be something else. Embrace the suck and be intel.

BLUF back at you - if there are no vacancies, it doesn't matter what you do. You are not going. If there are vacancies, then your best bet is to ensure your dream sheet is up to date and that you are fully qualified for the job you want. Do you have the ASI's you need and is your clearance current? Have you spoken to your platoon sergeant or first sergeant about this? Have you submitted a DA 4187 request for personnel action (this form may have changed: I've been out for 20 years!)?
A word of caution, though -- speaking from experience -- if you push too hard you can piss off the wrong people and not only NOT get your transfer but have your current assignment turn to crap before your very eyes.
I would not advise contacting the 35CMF Branch Manager unless you are E-6 or above. Doing so at a lower grade tends to be counter-productive. I wish you luck in your endeavors.

MOS? And even going to a MICO doesn't mean you will do intel work. Plenty of staff gigs, or training room, or arms room, or...