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.

I have been a 35F (well I came in when we were still 96Bs) and I have never been in a MI unit. My first unit was a combat en BN. Then I went to Cyber Command but I didn't really do any analyst work. I did targeting. I got there as it stood up. It sucked. Honestly. Then I went to Ft Riley and was in an infantry brigade. I was in the MICO for a little bit until they sent me to BDE S2. Then I was the BDE SARC until I came to Offutt AFB on a compassionate reassignment. Now I'm at STRATCOM and it's intel but I'm in a section where I'm the NCOIC and I don't do any analysis.

I have never met any other 35Fs who were in a MI unit their entire career. You are always going to do intel at some point no matter what unit you're in because you'll always be in the S2. Yes the most of your time in garrison is doing personnel security, ISOPREP and bs. But if your unit deploys or when you go to the field, you'll do intel. 35Fs can literally go to any unit. Anywhere. Trust me you don't want to go to a MI unit from what I've heard of them and you might not even do intel stuff there because everyone is intel. I know someone in a MI unit and she works in the orderly room - as a 35F. If you go to a non MI unit you're likely only going to be in the S2 as a 35F. It really helps to work at different types of units as a 35F in my opinion.

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.