Can my unit make me come in to work while I’m attending blc?

Your place of duty is your NCOES. You need to bring this up to your SGM

No, you are not required to go in. You are on orders to BLC. There is no regulation that allows your unit to force you to come in when you're on orders to NCOES

Technically, you are TDY to your NCOES and fall under the command of the academy. You are assigned on orders to the school, with a report date and an end date.

Your orders to BLC essentially attach you to the Academy for the duration of the course. In essence, you don't belong to your unit right now.
They are just expecting you to not fight and give in and show up because you don't know any better (units use that ploy a LOT).
I'd love to see the phone and email chain of those trying to do this. I'm guessing it went like this. "Hey, we're missing a PEQ, so call everyone in and look for it". as that filters down the chain some E5 or E6 sees that is call in everyone at school, leave, deployment, chemo, jail, taliban training camp etc to come in and look.....because they don't know how to think and are still thinking like joes...

To further clarify, NCO Academies and other schools on post have a memorandum of agreement, or make the unit sign a memorandum of agreement, stating that the Soldier belongs to the school house 100% during the course. This memo is submitted as part of your packet, if there isn't already a standing post policy in place. The purpose is to prevent exactly this type of thing from happening. If your unit hinders your school it can have lasting and career ending effects on a Soldier when that school is an NCOES.

Are you a member of the unit or not?
Doesn’t sound like it

Not sure it is allowed or not, but certainly shitty to make someone do... BLC requires a lot of after hours work. I would talk with you FLL and let them know of all your after hour commitments with BLC and request to not come in. However, the other side of that coin is as an NCO; the expectations is we are always ready for whatever we need to do and the workday end, when it ends... Hope it works out for you.

Everyone, including myself, agrees you have no obligation to return to your unit. Now that we know that, why are you even being approached? Was the PEQ in your custody recently? Did you, by your billet, have some involvement in the circumstances surrounding the disappearance? No, you shouldn't be expected to roaming around in the boonies turning over leaves looking for it, but perhaps an hour of your time could clear up any ambiguity about your having knowledge of the PEQs disappearance. Might prevent your being tied up for a longer period of time when the person assigned to officially investigate the disappearance is assigned.

NCOES is a 1059 producing school, which gives your unit the ability to account for time you spent temporarily assigned to another unit. When you are attending that school, you belong to TRADOC.

Tell your SGL, they can bring it up to the commandant.

If you're on orders to a school, your Command should respect that, unless situation dictates otherwise. No idea on Army.