What exactly does a CBRN Section do at the battalion level?

I was a CBRN SPC for an engineering Headquarters and Support Company when I was active duty as well as with a construction line company during my first reserve unit. So I have some insight into what you might be doing.

Chances are very high that 75% of the time you will be involved with the S3 doing some amount of OPS, or working with S2 with CBRN threat assessments. Engineering units often have a lot of large equipment. You may be called upon to provide guidance if your BN is asked to provide direct support large scale decon efforts. On the flip side, decon for your BN equipment, across the line units, can be quite a task and you would have a large hand in helping to determine site selection and integrating with whatever CBRN unit is part of your maneuver support element.

Outside tactical responsibilities, the primary role of the BN CBRN NCO is to make sure that the line companies are maintaining CBRN readiness training. A BN CBRN NCO should conduct regular meetings with the junior CBRN Soldiers in the line companies to determine how much training is being done and often to act as a senior level influencer to convince these Company level command teams to make the time to conduct CBRN training. CSM William Everroad Has already touched on other things.

By the way, I have the latest mask confidence exercise (gas chamber) protocol that was developed by the Chemical School. If you want, I am happy to provide it. Message me if you want me to email that to you.

Training, as well as "training," inventory, Supervising subordinates, and CE. How does a Specialist know? Because as an E-2, I filled an E-7 slot @ 62nd Med Grp., Ft. Lewis after "testing the waters" with the 369th Chem Co. @ Ft. Bliss, USAR.
Best of luck...

SSG (Join to see) it depends on the Battalion, their MTOE, and their TACSOP.
For many BNs, the CBRN section is nested with the torch when they setup the BN CP (which includes the TOC). They would be responsible for working with S2 to provide mitigation measures for any CBRN threat assessment such as setting up detection systems and to some extent decontamination sites. They work with supply for the resupply and maintenance of CBRN equipment across the BN (think MOPP gear, decon and detection equipment). They assist the BN staff during SAVs and inspection of CBRN capabilities for organic units. They would most likely be the BN point of contact for gas chamber training (depending on who is responsible for conducting the training and what base you are at).
Depending on the BN SOPs, your section should have some battle drills during torch operations, CBRN attacks, and deconstructions site operation.
Generally, if there is no CBRN threat or the work is done, they become staff duty in the TOC, guard/KP/RTO depending on the strength of the HQ and what equipment they have assigned on the MTOE.
The CBRN NCO would provide SME advise to the BN CDR (during C&S or BUBs) regarding CBRN threats and mitigation measures as well as decontamination operations.