How often does a 68A deploy and what MOS do they get stationed in during a deployment?

SPC (Join to see) you are most likely going to be in a CSH. You can use your CAC card and pull MTOE information from USAFMSA via FMSweb to see where 68As are authorized.

Here's a link from a 68A :
https://www.reddit.com/r/army/comments/6c0z2h/68a_biomedical_equipment_technician_a_brief/

I am late to the party, but maybe I can help other late comers.

As a 68A, your daily life and chances of deployment will vary depending on the type of unit you are stationed with:

Combat Support Hospital (CSH) - A CSH will have its own BMET shop usually consisting anywhere from 2-8 BMETs, along with a Warrant Officer. Whenver the CSH deploys, your entire shop is going with it. You will service the CSH's equipment, and some of the local unit's medical equipment as well.

Military Community Hospital/MEDDAC/Clinic - This is pretty much a 9-5 job. Hours may vary slightly, but this is the best place to learn the ins and outs of your job and gain experience. MEDDACs are usually attached to a hospital, but not always. (In Germany I know there exists a MEDDAC that services units all over the country.) And not every hospital has a MEDDAC, even though they have a biomed shop. (I don't know who makes the rules deciding what is considerdd a MEDDAC or not.) If you work for a clinic, usually it is a one-man shop and most of the equipment will be under contract. (Guess who's job it is to set up times with the vendor technicians to come out and service the equipment.)

Medical Logistics Company (MED LOG) - Depending on how well this unit functions, you may be bored with nothing to do except Motorpool Mondays, or a small team of 68As and 68Js may be constantly sent out to service equipment and provide supplies for units. Usually, they have more 68As and 68Js than they know what to do with. If a CSH or BSB needs assistance because they lack 68As, this is where they will request assistance from.

Brigade Support Battalion (BSB) - The Biomed Shop with these unit usually consists of a one or two-man shop. You service all the medical equipment for an entire battalion. Business can be slow or busy depending on the month. The most complicated equipment you will have to deal with here is usually a portable x-ray or ultrasound machine. (You may end up stuck as a make-shift generator mechanic as well.)

Unlike a lot of other MOS's, 68As do their job regardless of whether they are deployed or not. (Other MOS's train now so they can do their job when they deploy.) If the unit deploys, you are going with them. If your unit has a bit of history where bad things happened (i.e. someone went nuts and did bad stuff during deployment), the only deployments you can look forward to are NTC rotations.

MED LOGs can deploy as a single unit, or they can send small teams of 68As. If they are sending small teams, your chances of deploying are dependent on how well you know the job.

Hospitals/MEDDACs/Clinics are slightly different. The unit itself does not deploy because of the nature of their mission. However, you can get pulled and attached to another unit that might need you. Chances of you deploying from one of these units is slightly lower because they will fight to keep you there as they need you to do your job every day. In one MEDDAC I was stationed with, a 68A was attached to a unit and deployed. To fill his slot until he returned, they activated a 68A reservist.

Also keep in mind, you can be deployed for reasons that have nothing to do with your actual MOS. A 68J I knew years ago was deployed to Ukraine because she came from there and spoke the local language.